diff --git a/doc/equations/acosh1.svg b/doc/equations/acosh1.svg index c9ba67d3b..4d1eba0f1 100644 --- a/doc/equations/acosh1.svg +++ b/doc/equations/acosh1.svg @@ -1,2 +1,2 @@ - + acosh(x)=ln(x+x2−1) \ No newline at end of file diff --git a/doc/equations/acosh2.svg b/doc/equations/acosh2.svg index 383661b3c..cf0c65815 100644 --- a/doc/equations/acosh2.svg +++ b/doc/equations/acosh2.svg @@ -1,2 +1,2 @@ - + acosh(x)≈ln(2x);x>1ε \ No newline at end of file diff --git a/doc/equations/acosh3.svg b/doc/equations/acosh3.svg index c79a4d132..0edf76f50 100644 --- a/doc/equations/acosh3.svg +++ b/doc/equations/acosh3.svg @@ -1,2 +1,2 @@ - + acosh(x)=log1p(y+y2+2y);y=x−1 \ No newline at end of file diff --git a/doc/equations/acosh4.svg b/doc/equations/acosh4.svg index 293bcf48d..7e9af177e 100644 --- a/doc/equations/acosh4.svg +++ b/doc/equations/acosh4.svg @@ -1,2 +1,2 @@ - + acosh(x)≈2y(1−y12+3y2160);y=x−1∧y<ε \ No newline at end of file diff --git a/doc/equations/airy.svg b/doc/equations/airy.svg index 3ec9815b4..c8e828cc4 100644 --- a/doc/equations/airy.svg +++ b/doc/equations/airy.svg @@ -1,2 +1,2 @@ - + d2wdz2=zw;w=Ai(z),Bi(z),Ai(ze±2πi3) \ No newline at end of file diff --git a/doc/equations/airy_ai.svg b/doc/equations/airy_ai.svg index fdb08f67c..eee3ed5af 100644 --- a/doc/equations/airy_ai.svg +++ b/doc/equations/airy_ai.svg @@ -1,2 +1,2 @@ - + Ai(0)=1323Γ(23)Ai(z)=π−1z3K±13(ζ);ζ=23z23Ai(−z)=(z3)(J13(ζ)+J−13(ζ)) \ No newline at end of file diff --git a/doc/equations/airy_aip.svg b/doc/equations/airy_aip.svg index f55c76657..ce6ee10fc 100644 --- a/doc/equations/airy_aip.svg +++ b/doc/equations/airy_aip.svg @@ -1,2 +1,2 @@ - + Ai′(0)=−1313Γ(13)Ai′(z)=zπ3K±23(ζ);ζ=23z23Ai′(−z)=z3(J23(ζ)−J−23(ζ)) \ No newline at end of file diff --git a/doc/equations/airy_bi.svg b/doc/equations/airy_bi.svg index 44e6efcae..3105486fe 100644 --- a/doc/equations/airy_bi.svg +++ b/doc/equations/airy_bi.svg @@ -1,2 +1,2 @@ - + Bi(0)=1316Γ(23)Bi(z)=z3(I13(ζ)+I−13(ζ));ζ=23z23Bi(−z)=z3(J−13(ζ)−J13(ζ)) \ No newline at end of file diff --git a/doc/equations/airy_bip.svg b/doc/equations/airy_bip.svg index 311e43a55..8c28f3ac3 100644 --- a/doc/equations/airy_bip.svg +++ b/doc/equations/airy_bip.svg @@ -1,2 +1,2 @@ - + Bi′(0)=316Γ(13)Bi′(z)=z3(I23(ζ)+I−23(ζ));ζ=23z23Bi′(−z)=z3(J−23(ζ)+J23(ζ)) \ No newline at end of file diff --git a/doc/equations/asinh1.svg b/doc/equations/asinh1.svg index 9bbf82950..96b8b9d5f 100644 --- a/doc/equations/asinh1.svg +++ b/doc/equations/asinh1.svg @@ -1,2 +1,2 @@ - + asinh(x)=ln(x+x2+1) \ No newline at end of file diff --git a/doc/equations/asinh2.svg b/doc/equations/asinh2.svg index 7842a15bc..5f708472b 100644 --- a/doc/equations/asinh2.svg +++ b/doc/equations/asinh2.svg @@ -1,2 +1,2 @@ - + asinh(x)≈ln(2x)+14x2;x>1ε \ No newline at end of file diff --git a/doc/equations/asinh3.svg b/doc/equations/asinh3.svg index 4de1cced6..bfc3cc119 100644 --- a/doc/equations/asinh3.svg +++ b/doc/equations/asinh3.svg @@ -1,2 +1,2 @@ - + asinh(x)≈x−x36;x<ε \ No newline at end of file diff --git a/doc/equations/asinh4.svg b/doc/equations/asinh4.svg index 5c11b5ea5..9376b2845 100644 --- a/doc/equations/asinh4.svg +++ b/doc/equations/asinh4.svg @@ -1,2 +1,2 @@ - + asinh(x)=log1p(x+sqrtp1m1(x2)) \ No newline at end of file diff --git a/doc/equations/atanh1.svg b/doc/equations/atanh1.svg index 4a84de680..ce5f9e64b 100644 --- a/doc/equations/atanh1.svg +++ b/doc/equations/atanh1.svg @@ -1,2 +1,2 @@ - + atanh(x)=ln(1+x1−x)2 \ No newline at end of file diff --git a/doc/equations/atanh2.svg b/doc/equations/atanh2.svg index dab81641a..e67270449 100644 --- a/doc/equations/atanh2.svg +++ b/doc/equations/atanh2.svg @@ -1,2 +1,2 @@ - + atanh(x)≈x+x33;x<ε \ No newline at end of file diff --git a/doc/equations/atanh3.svg b/doc/equations/atanh3.svg index dfaaaab8d..e259e4c7e 100644 --- a/doc/equations/atanh3.svg +++ b/doc/equations/atanh3.svg @@ -1,2 +1,2 @@ - + atanh(x)=log1p(x)−log1p(−x)2 \ No newline at end of file diff --git a/doc/equations/bessel1.svg b/doc/equations/bessel1.svg index 64d8e1eee..9e8646327 100644 --- a/doc/equations/bessel1.svg +++ b/doc/equations/bessel1.svg @@ -1,2 +1,2 @@ - + z2d2udz2+zdudz+(z2−ν2)u=0 \ No newline at end of file diff --git a/doc/equations/bessel10.svg b/doc/equations/bessel10.svg index 8e2c4cd10..9c9ebe520 100644 --- a/doc/equations/bessel10.svg +++ b/doc/equations/bessel10.svg @@ -1,2 +1,2 @@ - + Y−ν(z)=sin(νπ)Jν(z)+cos(νπ)Yν(z) \ No newline at end of file diff --git a/doc/equations/bessel11.svg b/doc/equations/bessel11.svg index 6ec330da9..60069bdeb 100644 --- a/doc/equations/bessel11.svg +++ b/doc/equations/bessel11.svg @@ -1,2 +1,2 @@ - + CF1:fν=Jν+1Jν=12(ν+1)x−12(ν+2)x−⋅⋅⋅ \ No newline at end of file diff --git a/doc/equations/bessel12.svg b/doc/equations/bessel12.svg index a46af54da..2afbc996e 100644 --- a/doc/equations/bessel12.svg +++ b/doc/equations/bessel12.svg @@ -1,2 +1,2 @@ - + CF2:p+iq=Jν′+iYν′Jν+iYν=(i−12x)+ix[(12)2−ν22(x+i)+(32)2−ν22(x+2i)+⋅⋅⋅] \ No newline at end of file diff --git a/doc/equations/bessel13.svg b/doc/equations/bessel13.svg index 15c2cbcf6..3a67fe8f3 100644 --- a/doc/equations/bessel13.svg +++ b/doc/equations/bessel13.svg @@ -1,2 +1,2 @@ - + Jμ=±(Wq+γ(p−fμ))12Jμ+1=Jμ(μx−fμ)Yμ=γJμYμ+1=Yμ(μx−p−qγ) \ No newline at end of file diff --git a/doc/equations/bessel14.svg b/doc/equations/bessel14.svg index e53a3203a..96b066e2a 100644 --- a/doc/equations/bessel14.svg +++ b/doc/equations/bessel14.svg @@ -1,2 +1,2 @@ - + γ=p−fμq \ No newline at end of file diff --git a/doc/equations/bessel15.svg b/doc/equations/bessel15.svg index a9a68951e..a69f57e91 100644 --- a/doc/equations/bessel15.svg +++ b/doc/equations/bessel15.svg @@ -1,2 +1,2 @@ - + Yμ=−∑k=0∞ckgkYμ+1=−2x∑k=0∞ckhk \ No newline at end of file diff --git a/doc/equations/bessel16.svg b/doc/equations/bessel16.svg index bc57fae63..bd5f3644f 100644 --- a/doc/equations/bessel16.svg +++ b/doc/equations/bessel16.svg @@ -1,2 +1,2 @@ - + ck=1k!(−x24)k \ No newline at end of file diff --git a/doc/equations/bessel2.svg b/doc/equations/bessel2.svg index 018061483..85b073203 100644 --- a/doc/equations/bessel2.svg +++ b/doc/equations/bessel2.svg @@ -1,2 +1,2 @@ - + Jν(z)=(12z)ν∑k=0∞(−14z2)kk!Γ(ν+k+1) \ No newline at end of file diff --git a/doc/equations/bessel3.svg b/doc/equations/bessel3.svg index f3f7f41a8..35f57a2be 100644 --- a/doc/equations/bessel3.svg +++ b/doc/equations/bessel3.svg @@ -1,2 +1,2 @@ - + Yν(z)=Jν(z)cos(νπ)−J−ν(z)sin(νπ) \ No newline at end of file diff --git a/doc/equations/bessel4.svg b/doc/equations/bessel4.svg index 2cc92987f..42d1c2720 100644 --- a/doc/equations/bessel4.svg +++ b/doc/equations/bessel4.svg @@ -1,2 +1,2 @@ - + Jν+1(z)=2νzJν(z)−Jν−1(z) \ No newline at end of file diff --git a/doc/equations/bessel5.svg b/doc/equations/bessel5.svg index 13c579731..0c5d20173 100644 --- a/doc/equations/bessel5.svg +++ b/doc/equations/bessel5.svg @@ -1,2 +1,2 @@ - + Yν+1(z)=2νzYν(z)−Yν−1(z) \ No newline at end of file diff --git a/doc/equations/bessel6.svg b/doc/equations/bessel6.svg index 9107b9f4f..88a05a787 100644 --- a/doc/equations/bessel6.svg +++ b/doc/equations/bessel6.svg @@ -1,2 +1,2 @@ - + Jν′(z)=νzJν(z)−Jν+1(z) \ No newline at end of file diff --git a/doc/equations/bessel7.svg b/doc/equations/bessel7.svg index 707b8ff75..0acb6f9ce 100644 --- a/doc/equations/bessel7.svg +++ b/doc/equations/bessel7.svg @@ -1,2 +1,2 @@ - + Yν′(z)=νzYν(z)−Yν+1(z) \ No newline at end of file diff --git a/doc/equations/bessel8.svg b/doc/equations/bessel8.svg index a220f5bf0..ffa660c9d 100644 --- a/doc/equations/bessel8.svg +++ b/doc/equations/bessel8.svg @@ -1,2 +1,2 @@ - + W=Jν(z)Yν′(z)−Yν(z)Jν′(z)=Yν(z)Jν+1(z)−Jν(z)Yν+1(z)=2πz \ No newline at end of file diff --git a/doc/equations/bessel9.svg b/doc/equations/bessel9.svg index fc54da15a..9049ce437 100644 --- a/doc/equations/bessel9.svg +++ b/doc/equations/bessel9.svg @@ -1,2 +1,2 @@ - + J−ν(z)=cos(νπ)Jν(z)−sin(νπ)Yν(z) \ No newline at end of file diff --git a/doc/equations/bessel_y0_small_z.svg b/doc/equations/bessel_y0_small_z.svg index 2a53acc19..62fe97a6b 100644 --- a/doc/equations/bessel_y0_small_z.svg +++ b/doc/equations/bessel_y0_small_z.svg @@ -1,2 +1,2 @@ - + Y0(z)=2π(log(z2)+γ);z<ε \ No newline at end of file diff --git a/doc/equations/bessel_y1_small_z.svg b/doc/equations/bessel_y1_small_z.svg index ef74f41c4..8647e5577 100644 --- a/doc/equations/bessel_y1_small_z.svg +++ b/doc/equations/bessel_y1_small_z.svg @@ -1,2 +1,2 @@ - + Y1(z)=zπlog(z2)−2πz−z2π(1−2γ);z<ε \ No newline at end of file diff --git a/doc/equations/bessel_y2_small_z.svg b/doc/equations/bessel_y2_small_z.svg index 3252d3db1..5f78563cd 100644 --- a/doc/equations/bessel_y2_small_z.svg +++ b/doc/equations/bessel_y2_small_z.svg @@ -1,2 +1,2 @@ - + Y2=−z28π(32−2γ)−4πz2+z24πlog(z2);z<ε \ No newline at end of file diff --git a/doc/equations/bessel_yn_small_z.svg b/doc/equations/bessel_yn_small_z.svg index 4a8b2a285..2174a1db7 100644 --- a/doc/equations/bessel_yn_small_z.svg +++ b/doc/equations/bessel_yn_small_z.svg @@ -1,2 +1,2 @@ - + Yn(z)=−(n−1)!π(z2)−n;z<ε∧n>2 \ No newline at end of file diff --git a/doc/equations/bessel_yv_small_z.svg b/doc/equations/bessel_yv_small_z.svg index cba561244..310a4e2b9 100644 --- a/doc/equations/bessel_yv_small_z.svg +++ b/doc/equations/bessel_yv_small_z.svg @@ -1,2 +1,2 @@ - + Yv(z)=−Γ(v)π∑k=0∞(−1)k(z2)2k−v(1−v)kk!−Γ(−v)cos(vπ)π∑k=0∞(−1)k(z2)2k+v(v+1)kk!;v∉ℤ \ No newline at end of file diff --git a/doc/equations/beta1.svg b/doc/equations/beta1.svg index 67d24a003..888512b04 100644 --- a/doc/equations/beta1.svg +++ b/doc/equations/beta1.svg @@ -1,2 +1,2 @@ - + beta(a,b)=B(a,b)=Γ(a)Γ(b)Γ(a+b) \ No newline at end of file diff --git a/doc/equations/beta2.svg b/doc/equations/beta2.svg index 8eebc13d5..5a4de9688 100644 --- a/doc/equations/beta2.svg +++ b/doc/equations/beta2.svg @@ -1,2 +1,2 @@ - + beta(a,b)=(a+g−0.5a+b+g−0.5)a−0.5(b+g−0.5a+b+g−0.5)beb+g−0.5L(a)L(b)L(c) \ No newline at end of file diff --git a/doc/equations/beta3.svg b/doc/equations/beta3.svg index 73250d4c8..a8a3a68a4 100644 --- a/doc/equations/beta3.svg +++ b/doc/equations/beta3.svg @@ -1,2 +1,2 @@ - + beta(a,b)=(a+g−0.5a+b+g−0.5)a−b−0.5((a+g−0.5)(b+g−0.5)(a+b+g−0.5)2)beb+g−0.5L(a)L(b)L(c) \ No newline at end of file diff --git a/doc/equations/beta4.svg b/doc/equations/beta4.svg index f130637eb..1b9b960c1 100644 --- a/doc/equations/beta4.svg +++ b/doc/equations/beta4.svg @@ -1,2 +1,2 @@ - + beta(a,b)=(a+b)bbeta(a,b+1) \ No newline at end of file diff --git a/doc/equations/beta5.svg b/doc/equations/beta5.svg index 7187419cb..26958f9a0 100644 --- a/doc/equations/beta5.svg +++ b/doc/equations/beta5.svg @@ -1,2 +1,2 @@ - + beta(a,b)=(a+b)(a+b+1)abbeta(a+1,b+1) \ No newline at end of file diff --git a/doc/equations/beta6.svg b/doc/equations/beta6.svg index 64683ba66..92dfd791a 100644 --- a/doc/equations/beta6.svg +++ b/doc/equations/beta6.svg @@ -1,2 +1,2 @@ - + ifa≫banda+b=athen:beta(a,b)=Γ(b) \ No newline at end of file diff --git a/doc/equations/beta7.svg b/doc/equations/beta7.svg index ee8feaf66..1ee0c7585 100644 --- a/doc/equations/beta7.svg +++ b/doc/equations/beta7.svg @@ -1,2 +1,2 @@ - + ifa=1then:beta(a,b)=1b \ No newline at end of file diff --git a/doc/equations/beta8.svg b/doc/equations/beta8.svg index a059630be..2f78d20f5 100644 --- a/doc/equations/beta8.svg +++ b/doc/equations/beta8.svg @@ -1,2 +1,2 @@ - + elc−la−lb(lalc)a(lblc)b \ No newline at end of file diff --git a/doc/equations/beta_dist_kurtosis.svg b/doc/equations/beta_dist_kurtosis.svg index 66d0fa779..2cb783ed5 100644 --- a/doc/equations/beta_dist_kurtosis.svg +++ b/doc/equations/beta_dist_kurtosis.svg @@ -1,2 +1,2 @@ - + 6α3−α2(2β−1)+β2(β−1)−2αβ(β+2)αβ(α+β+2)(α+β+3) \ No newline at end of file diff --git a/doc/equations/binomial_ref1.svg b/doc/equations/binomial_ref1.svg index ec7cef8f8..3138ee207 100644 --- a/doc/equations/binomial_ref1.svg +++ b/doc/equations/binomial_ref1.svg @@ -1,2 +1,2 @@ - + f(k;n,p)=nCkpk(1−p)n−k=n!k!(n−k)!pk(1−p)n−k=Γ(n+1)Γ(k+1)Γ(n−k+1)pk(1−p)n−k=pk(1−p)n−kB(k+1,n−k+1)(n+1) \ No newline at end of file diff --git a/doc/equations/binomial_ref2.svg b/doc/equations/binomial_ref2.svg index 25b7e9938..23975bd2c 100644 --- a/doc/equations/binomial_ref2.svg +++ b/doc/equations/binomial_ref2.svg @@ -1,2 +1,2 @@ - + f(k;n,p)=nCkpk(1−p)n−k=n!k!(n−k)!pk(1−p)n−k \ No newline at end of file diff --git a/doc/equations/cauchy_ref1.svg b/doc/equations/cauchy_ref1.svg index ee6c6a8a7..6bf7cf8af 100644 --- a/doc/equations/cauchy_ref1.svg +++ b/doc/equations/cauchy_ref1.svg @@ -1,2 +1,2 @@ - + f(x;x0,γ)=1π(γ(x−x0)2+γ2) \ No newline at end of file diff --git a/doc/equations/chf.svg b/doc/equations/chf.svg index b2e59a7a4..8bb1c5c3a 100644 --- a/doc/equations/chf.svg +++ b/doc/equations/chf.svg @@ -1,2 +1,2 @@ - + chf(dist,x)=H(x)=∫−∞xh(μ)dμ \ No newline at end of file diff --git a/doc/equations/chi_squ_ref1.svg b/doc/equations/chi_squ_ref1.svg index bf94addcc..b335afe3e 100644 --- a/doc/equations/chi_squ_ref1.svg +++ b/doc/equations/chi_squ_ref1.svg @@ -1,2 +1,2 @@ - + Q=∑i=1ν(χi−νiσi)2 \ No newline at end of file diff --git a/doc/equations/chi_squ_tut1.svg b/doc/equations/chi_squ_tut1.svg index ee6be2210..388ec4d68 100644 --- a/doc/equations/chi_squ_tut1.svg +++ b/doc/equations/chi_squ_tut1.svg @@ -1,2 +1,2 @@ - + (N−1)s2χ(α2,N−1)2≤σ≤(N−1)s2χ(1−α2,N−1)2 \ No newline at end of file diff --git a/doc/equations/chi_squ_tut2.svg b/doc/equations/chi_squ_tut2.svg index 03475f0e6..6786e446b 100644 --- a/doc/equations/chi_squ_tut2.svg +++ b/doc/equations/chi_squ_tut2.svg @@ -1,2 +1,2 @@ - + χ(α2,N−1)2 \ No newline at end of file diff --git a/doc/equations/chi_squ_tut3.svg b/doc/equations/chi_squ_tut3.svg index aa10b98a0..9077391bb 100644 --- a/doc/equations/chi_squ_tut3.svg +++ b/doc/equations/chi_squ_tut3.svg @@ -1,2 +1,2 @@ - + χ(1−α2,N−1)2 \ No newline at end of file diff --git a/doc/equations/derivative1.svg b/doc/equations/derivative1.svg index b976dcfb6..6581972af 100644 --- a/doc/equations/derivative1.svg +++ b/doc/equations/derivative1.svg @@ -1,2 +1,2 @@ - + gamma_p_derivative(a,x)=∂∂xP(a,x)=e−xxa−1Γ(a) \ No newline at end of file diff --git a/doc/equations/derivative2.svg b/doc/equations/derivative2.svg index 53612b144..336059f4b 100644 --- a/doc/equations/derivative2.svg +++ b/doc/equations/derivative2.svg @@ -1,2 +1,2 @@ - + ibeta_derivative(a,b,x)=∂∂xIx(a,b)=(1−x)b−1xa−1B(a,b) \ No newline at end of file diff --git a/doc/equations/digamma1.svg b/doc/equations/digamma1.svg index e17a78d3c..034d066d3 100644 --- a/doc/equations/digamma1.svg +++ b/doc/equations/digamma1.svg @@ -1,2 +1,2 @@ - + ψ(x)=ddxln(Γ(x))=Γ′(x)Γ(x) \ No newline at end of file diff --git a/doc/equations/digamma2.svg b/doc/equations/digamma2.svg index 7a77a35d5..b4db806c0 100644 --- a/doc/equations/digamma2.svg +++ b/doc/equations/digamma2.svg @@ -1,2 +1,2 @@ - + ψ(x)=ln(x)+12x−∑n=1∞B2n2nx2n \ No newline at end of file diff --git a/doc/equations/digamma3.svg b/doc/equations/digamma3.svg index 0c6cf9ff0..7ab0de08d 100644 --- a/doc/equations/digamma3.svg +++ b/doc/equations/digamma3.svg @@ -1,2 +1,2 @@ - + ψ(x)=z−12x+g−12+ln(x+g−12)+P′(x)P(x)−Q′(x)Q(x)−1 \ No newline at end of file diff --git a/doc/equations/dist_tutorial1.svg b/doc/equations/dist_tutorial1.svg index 748ec731e..4c13d7b36 100644 --- a/doc/equations/dist_tutorial1.svg +++ b/doc/equations/dist_tutorial1.svg @@ -1,2 +1,2 @@ - + t=Sm1−Sm2sp1S n1+1S n2sp=(Sn1−1)Sd12+(Sn2−1)Sd22Sn1+Sn2−2ν=Sn1+Sn2−2 \ No newline at end of file diff --git a/doc/equations/dist_tutorial2.svg b/doc/equations/dist_tutorial2.svg index c2fb1f4b7..a3b2cd49e 100644 --- a/doc/equations/dist_tutorial2.svg +++ b/doc/equations/dist_tutorial2.svg @@ -1,2 +1,2 @@ - + t=Sm1−Sm2Sd12Sn1+Sd22Sn2 \ No newline at end of file diff --git a/doc/equations/dist_tutorial3.svg b/doc/equations/dist_tutorial3.svg index 87a4d2732..6067e09e9 100644 --- a/doc/equations/dist_tutorial3.svg +++ b/doc/equations/dist_tutorial3.svg @@ -1,2 +1,2 @@ - + ν=(Sd12Sn1+Sd22Sn2)2(Sd12Sn1)2(Sn1−1)+(Sd22Sn2)2(Sn2−1) \ No newline at end of file diff --git a/doc/equations/dist_tutorial4.svg b/doc/equations/dist_tutorial4.svg index 9d2634bc4..cdd9bafea 100644 --- a/doc/equations/dist_tutorial4.svg +++ b/doc/equations/dist_tutorial4.svg @@ -1,2 +1,2 @@ - + Ys±t(α2,N−1)sN \ No newline at end of file diff --git a/doc/equations/ellint1.svg b/doc/equations/ellint1.svg index 49d47565d..93ef606c1 100644 --- a/doc/equations/ellint1.svg +++ b/doc/equations/ellint1.svg @@ -1,2 +1,2 @@ - + ∫R(t,s)dt \ No newline at end of file diff --git a/doc/equations/ellint10.svg b/doc/equations/ellint10.svg index 1d9129c35..8c9141ac2 100644 --- a/doc/equations/ellint10.svg +++ b/doc/equations/ellint10.svg @@ -1,2 +1,2 @@ - + RD(x,y,z)=32∫0∞[(t+x)(t+y)]−12(t+z)−32dt \ No newline at end of file diff --git a/doc/equations/ellint11.svg b/doc/equations/ellint11.svg index 552c81c53..0864b1e11 100644 --- a/doc/equations/ellint11.svg +++ b/doc/equations/ellint11.svg @@ -1,2 +1,2 @@ - + RJ(x,y,z,p)=32∫0∞(t+p)−1[(t+x)(t+y)(t+z)]−12dt \ No newline at end of file diff --git a/doc/equations/ellint12.svg b/doc/equations/ellint12.svg index f2dd4b0ae..efc69fcd9 100644 --- a/doc/equations/ellint12.svg +++ b/doc/equations/ellint12.svg @@ -1,2 +1,2 @@ - + RC(x,y)=12∫0∞(t+x)−12(t+y)−1dt \ No newline at end of file diff --git a/doc/equations/ellint13.svg b/doc/equations/ellint13.svg index a1950fc99..6af1824a1 100644 --- a/doc/equations/ellint13.svg +++ b/doc/equations/ellint13.svg @@ -1,2 +1,2 @@ - + RF(x,y,z)=2RF(x+λ,y+λ,z+λ)=RF(x+λ4,y+λ4,z+λ4)λ=xy+yz+zx \ No newline at end of file diff --git a/doc/equations/ellint14.svg b/doc/equations/ellint14.svg index 0fbff6693..c582d9ee3 100644 --- a/doc/equations/ellint14.svg +++ b/doc/equations/ellint14.svg @@ -1,2 +1,2 @@ - + F(φ,k)=sinφRF(cos2φ,1−k2sin2φ,1)E(φ,k)=sinφRF(cos2φ,1−k2sin2φ,1)−13k2sin3φRD(cos2φ,1−k2sin2φ,1)Π(n,φ,k)=sinφRF(cos2φ,1−k2sin2φ,1)+13nsin3φRJ(cos2φ,1−k2sin2φ,1,1−nsin2φ) \ No newline at end of file diff --git a/doc/equations/ellint15.svg b/doc/equations/ellint15.svg index 0e9d4a739..00ce49f77 100644 --- a/doc/equations/ellint15.svg +++ b/doc/equations/ellint15.svg @@ -1,2 +1,2 @@ - + K(k)=RF(0,1−k2,1)E(k)=RF(0,1−k2,1)−13k2RD(0,1−k2,1)Π(n,k)=RF(0,1−k2,1)+13nRJ(0,1−k2,1,1−n) \ No newline at end of file diff --git a/doc/equations/ellint16.svg b/doc/equations/ellint16.svg index e20460912..d05ef2627 100644 --- a/doc/equations/ellint16.svg +++ b/doc/equations/ellint16.svg @@ -1,2 +1,2 @@ - + RF(x,x,x)=1x \ No newline at end of file diff --git a/doc/equations/ellint17.svg b/doc/equations/ellint17.svg index a2a34878f..0e617178c 100644 --- a/doc/equations/ellint17.svg +++ b/doc/equations/ellint17.svg @@ -1,2 +1,2 @@ - + (y+q)RJ(x,y,z,−q)=(p−y)RJ(x,y,z,p)−3RF(x,y,z)+3(xyzxz+pq)12RC(xz+pq,pq)with:q>0and:p=y+(z−y)(y−x)(y+q) \ No newline at end of file diff --git a/doc/equations/ellint18.svg b/doc/equations/ellint18.svg index 5bd74886d..63e90f5b8 100644 --- a/doc/equations/ellint18.svg +++ b/doc/equations/ellint18.svg @@ -1,2 +1,2 @@ - + RC(x,−y)=(xx+y)12RC(x+y,y) \ No newline at end of file diff --git a/doc/equations/ellint19.svg b/doc/equations/ellint19.svg index 8d2be44ab..903628ceb 100644 --- a/doc/equations/ellint19.svg +++ b/doc/equations/ellint19.svg @@ -1,2 +1,2 @@ - + F(−φ,k)=−F(φ,k)F(φ+mπ,k)=F(φ,k)+2mK(k)F(φ,k)=sinφRF(cos2φ,1−k2sin2φ,1) \ No newline at end of file diff --git a/doc/equations/ellint2.svg b/doc/equations/ellint2.svg index b5dba6caf..506401bd6 100644 --- a/doc/equations/ellint2.svg +++ b/doc/equations/ellint2.svg @@ -1,2 +1,2 @@ - + F(φ,k)=∫0φdθ1−k2sin2θ \ No newline at end of file diff --git a/doc/equations/ellint20.svg b/doc/equations/ellint20.svg index 956c34904..e82fcd737 100644 --- a/doc/equations/ellint20.svg +++ b/doc/equations/ellint20.svg @@ -1,2 +1,2 @@ - + K(k)=RF(0,1−k2,1) \ No newline at end of file diff --git a/doc/equations/ellint21.svg b/doc/equations/ellint21.svg index 21c90d2ff..fc39c89b0 100644 --- a/doc/equations/ellint21.svg +++ b/doc/equations/ellint21.svg @@ -1,2 +1,2 @@ - + E(−φ,k)=−E(φ,k)E(φ+mπ,k)=E(φ,k)+2mE(k);φ∉[0,π2]E(φ,k)=sinφRF(cos2φ,1−k2sin2φ,1)−13k2sin3φRD(cos2φ,1−k2sin2φ,1) \ No newline at end of file diff --git a/doc/equations/ellint22.svg b/doc/equations/ellint22.svg index 22dd0303f..c70931c94 100644 --- a/doc/equations/ellint22.svg +++ b/doc/equations/ellint22.svg @@ -1,2 +1,2 @@ - + E(k)=RF(0,1−k2,1)−13k2RD(0,1−k2,1) \ No newline at end of file diff --git a/doc/equations/ellint23.svg b/doc/equations/ellint23.svg index 88b5c4f70..37222adec 100644 --- a/doc/equations/ellint23.svg +++ b/doc/equations/ellint23.svg @@ -1,2 +1,2 @@ - + ∏(n,φ,0)=11−ntan−1(1−ntanφ);n<1=1n−1tanh−1(n−1tanφ);n>1=tanφ;n=1 \ No newline at end of file diff --git a/doc/equations/ellint24.svg b/doc/equations/ellint24.svg index 409c569d8..3a5ebdc80 100644 --- a/doc/equations/ellint24.svg +++ b/doc/equations/ellint24.svg @@ -1,2 +1,2 @@ - + (1−n)(1−k2n)∏(n,φ,k)=(1−N)(1−k2N)∏(N,φ,k)+k2p2F(φ,k)+tan−1(p22sin2φ?(φ))N=(k2−n)(1−n)p2=−n1−n(k2−n) \ No newline at end of file diff --git a/doc/equations/ellint25.svg b/doc/equations/ellint25.svg index f9d6e75d3..69548a507 100644 --- a/doc/equations/ellint25.svg +++ b/doc/equations/ellint25.svg @@ -1,2 +1,2 @@ - + ∏(n,φ,k)=sinφRF(cos2φ,1−k2sin2φ,1)+n3sin3φRJ(cos2φ,1−k2sin2φ,1,1−nsin2φ) \ No newline at end of file diff --git a/doc/equations/ellint26.svg b/doc/equations/ellint26.svg index cf7dace3c..2371edb44 100644 --- a/doc/equations/ellint26.svg +++ b/doc/equations/ellint26.svg @@ -1,2 +1,2 @@ - + ∏(n,k)=RF(0,1−k2,1)+n3RJ(0,1−k2,1,1−n) \ No newline at end of file diff --git a/doc/equations/ellint3.svg b/doc/equations/ellint3.svg index b53c79023..de38f44b0 100644 --- a/doc/equations/ellint3.svg +++ b/doc/equations/ellint3.svg @@ -1,2 +1,2 @@ - + E(φ,k)=∫0φ1−k2sin2θdθ \ No newline at end of file diff --git a/doc/equations/ellint4.svg b/doc/equations/ellint4.svg index dce0f2bd1..e3a195f84 100644 --- a/doc/equations/ellint4.svg +++ b/doc/equations/ellint4.svg @@ -1,2 +1,2 @@ - + Π(n,φ,k)=∫0φdθ(1−nsin2θ)1−k2sin2θ \ No newline at end of file diff --git a/doc/equations/ellint5.svg b/doc/equations/ellint5.svg index 80dcc0d1d..e9cece467 100644 --- a/doc/equations/ellint5.svg +++ b/doc/equations/ellint5.svg @@ -1,2 +1,2 @@ - + k=sinα,|k|≤1 \ No newline at end of file diff --git a/doc/equations/ellint6.svg b/doc/equations/ellint6.svg index f703a335f..402635aa3 100644 --- a/doc/equations/ellint6.svg +++ b/doc/equations/ellint6.svg @@ -1,2 +1,2 @@ - + K(k)=F(π2,k)=∫0π2dθ1−k2sin2θ \ No newline at end of file diff --git a/doc/equations/ellint7.svg b/doc/equations/ellint7.svg index 31973f136..29f78b6d3 100644 --- a/doc/equations/ellint7.svg +++ b/doc/equations/ellint7.svg @@ -1,2 +1,2 @@ - + E(k)=E(π2,k)=∫0π21−k2sin2θdθ \ No newline at end of file diff --git a/doc/equations/ellint8.svg b/doc/equations/ellint8.svg index 82051fc55..978be26e3 100644 --- a/doc/equations/ellint8.svg +++ b/doc/equations/ellint8.svg @@ -1,2 +1,2 @@ - + ∏(n,k)=∏(n,π2,k)=∫0π2dθ(1−nsin2θ)1−k2sin2θ \ No newline at end of file diff --git a/doc/equations/ellint9.svg b/doc/equations/ellint9.svg index 245279aca..92738a87d 100644 --- a/doc/equations/ellint9.svg +++ b/doc/equations/ellint9.svg @@ -1,2 +1,2 @@ - + RF(x,y,z)=12∫0∞[(t+x)(t+y)(t+z)]−12dt \ No newline at end of file diff --git a/doc/equations/erf1.svg b/doc/equations/erf1.svg index 333bc0237..d860f36c1 100644 --- a/doc/equations/erf1.svg +++ b/doc/equations/erf1.svg @@ -1,2 +1,2 @@ - + erf(z)=2π∫0ze−t2dt \ No newline at end of file diff --git a/doc/equations/erf2.svg b/doc/equations/erf2.svg index 79c294739..2183a2f88 100644 --- a/doc/equations/erf2.svg +++ b/doc/equations/erf2.svg @@ -1,2 +1,2 @@ - + erfc(z)=1−erf(z) \ No newline at end of file diff --git a/doc/equations/error1.svg b/doc/equations/error1.svg index 8aea178b5..82d601adb 100644 --- a/doc/equations/error1.svg +++ b/doc/equations/error1.svg @@ -1,2 +1,2 @@ - + max(|a−va|,|a−vv|) \ No newline at end of file diff --git a/doc/equations/error2.svg b/doc/equations/error2.svg index 812f51fd1..ae03b39f3 100644 --- a/doc/equations/error2.svg +++ b/doc/equations/error2.svg @@ -1,2 +1,2 @@ - + |a−va| \ No newline at end of file diff --git a/doc/equations/expint_i_1.svg b/doc/equations/expint_i_1.svg index 821f4e2e2..6121ede24 100644 --- a/doc/equations/expint_i_1.svg +++ b/doc/equations/expint_i_1.svg @@ -1,2 +1,2 @@ - + Ei(x)=−E1(−x)=∫−x∞e−tdtt \ No newline at end of file diff --git a/doc/equations/expint_i_2.svg b/doc/equations/expint_i_2.svg index bd5aa4ecc..b1868a5f3 100644 --- a/doc/equations/expint_i_2.svg +++ b/doc/equations/expint_i_2.svg @@ -1,2 +1,2 @@ - + Ei(z)=log(z)+γ+∑k=0∞zkkk! \ No newline at end of file diff --git a/doc/equations/expint_i_3.svg b/doc/equations/expint_i_3.svg index 6a054024e..a296a99e6 100644 --- a/doc/equations/expint_i_3.svg +++ b/doc/equations/expint_i_3.svg @@ -1,2 +1,2 @@ - + Ei(z)=log(zz0)+(z−z0)R(z3−1) \ No newline at end of file diff --git a/doc/equations/expint_i_4.svg b/doc/equations/expint_i_4.svg index a64e89423..9d26331ee 100644 --- a/doc/equations/expint_i_4.svg +++ b/doc/equations/expint_i_4.svg @@ -1,2 +1,2 @@ - + Ei(z)=z+ezz(c+R(t)) \ No newline at end of file diff --git a/doc/equations/expint_n_1.svg b/doc/equations/expint_n_1.svg index adcddb490..ee5ff2884 100644 --- a/doc/equations/expint_n_1.svg +++ b/doc/equations/expint_n_1.svg @@ -1,2 +1,2 @@ - + En(x)=∫1∞e−xtdttn \ No newline at end of file diff --git a/doc/equations/expint_n_2.svg b/doc/equations/expint_n_2.svg index 50ee895c0..10fdf84fd 100644 --- a/doc/equations/expint_n_2.svg +++ b/doc/equations/expint_n_2.svg @@ -1,2 +1,2 @@ - + En(x)=(−z)n−1(n−1)!(ψ(n)−log(z))−∑k=0,k≠n−1∞(−1)kzk(k−n+1)k! \ No newline at end of file diff --git a/doc/equations/expint_n_3.svg b/doc/equations/expint_n_3.svg index e293c713b..d24dfb405 100644 --- a/doc/equations/expint_n_3.svg +++ b/doc/equations/expint_n_3.svg @@ -1,2 +1,2 @@ - + En(x)=e−xn+x−n2+n+x−2(n+1)4+n+x−3(n+2)6+n+x−4(n+3)8+n+x−… \ No newline at end of file diff --git a/doc/equations/expint_n_4.svg b/doc/equations/expint_n_4.svg index c9d74cb54..694ae7469 100644 --- a/doc/equations/expint_n_4.svg +++ b/doc/equations/expint_n_4.svg @@ -1,2 +1,2 @@ - + E1(x)=x+log(x)+c+R(x) \ No newline at end of file diff --git a/doc/equations/expint_n_5.svg b/doc/equations/expint_n_5.svg index 5ab788944..bc1a7efa7 100644 --- a/doc/equations/expint_n_5.svg +++ b/doc/equations/expint_n_5.svg @@ -1,2 +1,2 @@ - + E1(x)=e−xx(1+R(1x)) \ No newline at end of file diff --git a/doc/equations/exponential_dist_ref1.svg b/doc/equations/exponential_dist_ref1.svg index d3f27c76a..e559d1aed 100644 --- a/doc/equations/exponential_dist_ref1.svg +++ b/doc/equations/exponential_dist_ref1.svg @@ -1,2 +1,2 @@ - + f(x)=λe−λx \ No newline at end of file diff --git a/doc/equations/fisher_pdf.svg b/doc/equations/fisher_pdf.svg index 329eb7d3c..e649c9ccc 100644 --- a/doc/equations/fisher_pdf.svg +++ b/doc/equations/fisher_pdf.svg @@ -1,2 +1,2 @@ - + fn,m(x)=mm2nn2xn2−1(m+nx)(n+m)2B(n2,m2) \ No newline at end of file diff --git a/doc/equations/fraction1.svg b/doc/equations/fraction1.svg index 3de5ddaec..7770ddeb6 100644 --- a/doc/equations/fraction1.svg +++ b/doc/equations/fraction1.svg @@ -1,2 +1,2 @@ - 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+ Γ(a)=(lae−l)(∑k=0∞lnak+1−+1l−a+1+c1d1+c2d2+c3d3+…);ck=k(a−k)∧dk=l−a+2k+1 \ No newline at end of file diff --git a/doc/equations/gamm3.svg b/doc/equations/gamm3.svg index 5946143ba..953be1c25 100644 --- a/doc/equations/gamm3.svg +++ b/doc/equations/gamm3.svg @@ -1,2 +1,2 @@ - + Γ(z)=Γ(z+1)z \ No newline at end of file diff --git a/doc/equations/gamm4.svg b/doc/equations/gamm4.svg index f87d45b61..48cbb1121 100644 --- a/doc/equations/gamm4.svg +++ b/doc/equations/gamm4.svg @@ -1,2 +1,2 @@ - + limz→0(Γ(z))=1z \ No newline at end of file diff --git a/doc/equations/gamm5.svg b/doc/equations/gamm5.svg index 4eb369b4d..7893a9b60 100644 --- a/doc/equations/gamm5.svg +++ b/doc/equations/gamm5.svg @@ -1,2 +1,2 @@ - + Γ(−z)=−πΓ(z)sin(πz)z \ No newline at end of file diff --git a/doc/equations/gamma_dist_ref1.svg b/doc/equations/gamma_dist_ref1.svg index 8ee2e0a87..634f368ef 100644 --- a/doc/equations/gamma_dist_ref1.svg +++ b/doc/equations/gamma_dist_ref1.svg @@ -1,2 +1,2 @@ - + f(x;k,θ)=xk−1e−xθθkΓ(k) \ No newline at end of file diff --git a/doc/equations/gamma_dist_ref2.svg b/doc/equations/gamma_dist_ref2.svg index ba6c53d21..e4a595737 100644 --- a/doc/equations/gamma_dist_ref2.svg +++ b/doc/equations/gamma_dist_ref2.svg @@ -1,2 +1,2 @@ - + f(x;α,β)=xα−1βαe−βxΓ(α) \ No newline at end of file diff --git a/doc/equations/gamma_ratio0.svg b/doc/equations/gamma_ratio0.svg index afbd4e9f3..a31e30d63 100644 --- a/doc/equations/gamma_ratio0.svg +++ b/doc/equations/gamma_ratio0.svg @@ -1,2 +1,2 @@ - + tgamma_ratio(a,b)=Γ(a)Γ(b) \ No newline at end of file diff --git a/doc/equations/gamma_ratio1.svg b/doc/equations/gamma_ratio1.svg index 4139afdcb..e8b0acd78 100644 --- a/doc/equations/gamma_ratio1.svg +++ b/doc/equations/gamma_ratio1.svg @@ -1,2 +1,2 @@ - + tgamma_delta_ratio(a,delta)=Γ(a)Γ(a+delta) \ No newline at end of file diff --git a/doc/equations/hankel1.svg b/doc/equations/hankel1.svg index 564245a82..e29216685 100644 --- a/doc/equations/hankel1.svg +++ b/doc/equations/hankel1.svg @@ -1,2 +1,2 @@ - + Jν(−z)=(−z)νz−νJν(z) \ No newline at end of file diff --git a/doc/equations/hankel2.svg b/doc/equations/hankel2.svg index ced038128..70f70ab69 100644 --- a/doc/equations/hankel2.svg +++ b/doc/equations/hankel2.svg @@ -1,2 +1,2 @@ - + Yν(−z)=zνYν(z)(−z)−ν+((−z)νz−ν−(−z)−νzν)Jν(z)cot(πν);ν∉ℤ \ No newline at end of file diff --git a/doc/equations/hankel3.svg b/doc/equations/hankel3.svg index 21a9bb6ee..a8b4eca20 100644 --- a/doc/equations/hankel3.svg +++ b/doc/equations/hankel3.svg @@ -1,2 +1,2 @@ - + Yν(−z)=(−1)ν(Yν(z)−2π(log(z)−log(−z))Jν(z));ν∈ℤ \ No newline at end of file diff --git a/doc/equations/hankel4.svg b/doc/equations/hankel4.svg index 1126b948e..24c7d9860 100644 --- a/doc/equations/hankel4.svg +++ b/doc/equations/hankel4.svg @@ -1,2 +1,2 @@ - + hv(1)(x)=π21xHv+12(1)(x) \ No newline at end of file diff --git a/doc/equations/hankel5.svg b/doc/equations/hankel5.svg index 3dd64979a..06d05e60b 100644 --- a/doc/equations/hankel5.svg +++ b/doc/equations/hankel5.svg @@ -1,2 +1,2 @@ - + hv(2)(x)=π21xHv+12(2)(x) \ No newline at end of file diff --git a/doc/equations/hazard.svg b/doc/equations/hazard.svg index 80ddee434..6145b431e 100644 --- a/doc/equations/hazard.svg +++ b/doc/equations/hazard.svg @@ -1,2 +1,2 @@ - + hazard(x)=h(x)=pdf(x)1−cdf(x) \ No newline at end of file diff --git a/doc/equations/hermite_0.svg b/doc/equations/hermite_0.svg index 64751fb17..00b1f7b11 100644 --- a/doc/equations/hermite_0.svg +++ b/doc/equations/hermite_0.svg @@ -1,2 +1,2 @@ - + hermite(x)=Hn(x)=(−1)nex2d2dx2e−x2 \ No newline at end of file diff --git a/doc/equations/hermite_1.svg b/doc/equations/hermite_1.svg index 64a76f0ba..4f8aa84e6 100644 --- a/doc/equations/hermite_1.svg +++ b/doc/equations/hermite_1.svg @@ -1,2 +1,2 @@ - + Hn+1(x)=2xHn(x)−2nHn−1(x) \ No newline at end of file diff --git a/doc/equations/hypergeometric1.svg b/doc/equations/hypergeometric1.svg index 8f273d9d3..584345b93 100644 --- a/doc/equations/hypergeometric1.svg +++ b/doc/equations/hypergeometric1.svg @@ -1,2 +1,2 @@ - + f(k;r,n,N)=n!r!(N−n)!(N−r)!N!k!(n−k)!(r−k)!(N−n−r+k)!;max(0,N−r−n+k)<=k<=min(r,n) \ No newline at end of file diff --git a/doc/equations/hypergeometric2.svg b/doc/equations/hypergeometric2.svg index b2c918eb5..319fc6666 100644 --- a/doc/equations/hypergeometric2.svg +++ b/doc/equations/hypergeometric2.svg @@ -1,2 +1,2 @@ - + N!=∏i=0pi<Npiei \ No newline at end of file diff --git a/doc/equations/hypergeometric3.svg b/doc/equations/hypergeometric3.svg index 2d53025e2..5b909c520 100644 --- a/doc/equations/hypergeometric3.svg +++ b/doc/equations/hypergeometric3.svg @@ -1,2 +1,2 @@ - + ei=∑j=1pij≤Nflοor(Npij) \ No newline at end of file diff --git a/doc/equations/hypergeometric4.svg b/doc/equations/hypergeometric4.svg index 8814d8618..f24e22575 100644 --- a/doc/equations/hypergeometric4.svg +++ b/doc/equations/hypergeometric4.svg @@ -1,2 +1,2 @@ - + f(k;r,n,N)=∏i=0pi<Npiei \ No newline at end of file diff --git a/doc/equations/hypergeometric5.svg b/doc/equations/hypergeometric5.svg index 143e46d5b..7ef5aa9ca 100644 --- a/doc/equations/hypergeometric5.svg +++ b/doc/equations/hypergeometric5.svg @@ -1,2 +1,2 @@ - + f(k+1;r,n,N)=(n−k)(r−k)(k+1)(N−n−r+k+1)f(k;r,n,N)f(k−1;r,n,N)=x(N−n−r+k)(n−k+1)(r−k+1)f(k;r,n,N) \ No newline at end of file diff --git a/doc/equations/hypergeometric6.svg b/doc/equations/hypergeometric6.svg index ee36304bd..677c268e1 100644 --- a/doc/equations/hypergeometric6.svg +++ b/doc/equations/hypergeometric6.svg @@ -1,2 +1,2 @@ - + mean=rnNmode=floor((r+1)(n+1)N+2)variance=r(nN)(1−nN)(N−r)(N−1)skewness=(N−2n)(N−1)(N−2r)rn(N−n)(N−r)(N−2)kurtosis excess=(N2(N−1)r(N−2)(N−3)(N−r))(N(N+1)−6N(N−r)n(N−n)+3r(N−r)(N+6)N2−6) \ No newline at end of file diff --git a/doc/equations/hypot.svg b/doc/equations/hypot.svg index 4c3a8acc8..a040d632a 100644 --- a/doc/equations/hypot.svg +++ b/doc/equations/hypot.svg @@ -1,2 +1,2 @@ - + hypot(x,y)=x2+y2 \ No newline at end of file diff --git a/doc/equations/hypot2.svg b/doc/equations/hypot2.svg index ccd9499be..0cdd39434 100644 --- a/doc/equations/hypot2.svg +++ b/doc/equations/hypot2.svg @@ -1,2 +1,2 @@ - + hypot(x,y)=x1+(yx)2 \ No newline at end of file diff --git a/doc/equations/ibeta1.svg b/doc/equations/ibeta1.svg index 31de12f8e..7fd152bf1 100644 --- a/doc/equations/ibeta1.svg +++ b/doc/equations/ibeta1.svg @@ -1,2 +1,2 @@ - + beta(a,b,x)=Bx(a,b)=∫0xta−1(1−t)b−1dt \ No newline at end of file diff --git a/doc/equations/ibeta10.svg b/doc/equations/ibeta10.svg index e644520bc..5a1230a83 100644 --- a/doc/equations/ibeta10.svg +++ b/doc/equations/ibeta10.svg @@ -1,2 +1,2 @@ - + Ix(a,b)=Ix(a+n,b)+xa(1−x)b∑j=1nΓ(a+b+j−1)Γ(b)Γ(a+j)xj−1=Ix(a+n,b)+xa(1−x)ba∑j=0n−1(a+b)j−(a+1)j−xj \ No newline at end of file diff --git a/doc/equations/ibeta11.svg b/doc/equations/ibeta11.svg index 958442197..7efa9e0d1 100644 --- a/doc/equations/ibeta11.svg +++ b/doc/equations/ibeta11.svg @@ -1,2 +1,2 @@ - + Bx(a,b)=(a+b)n−an−Bx(a+n,b)+xa(1−x)ba∑j=0n−1(a+b)j−(a+1)j−xj \ No newline at end of file diff --git a/doc/equations/ibeta12.svg b/doc/equations/ibeta12.svg index a3eb39416..e5aed334b 100644 --- a/doc/equations/ibeta12.svg +++ b/doc/equations/ibeta12.svg @@ -1,2 +1,2 @@ - + Ix(a,b)=∑i=k+1NN!i!(N−i)!xiy(N−i);k=a−1,N=a+b−1 \ No newline at end of file diff --git a/doc/equations/ibeta2.svg b/doc/equations/ibeta2.svg index f7c3fbb75..850b55f0c 100644 --- a/doc/equations/ibeta2.svg +++ b/doc/equations/ibeta2.svg @@ -1,2 +1,2 @@ - + betac(a,b,x)=1−Bx(a,b)=B1−x(b,a) \ No newline at end of file diff --git a/doc/equations/ibeta3.svg b/doc/equations/ibeta3.svg index f23c66b39..a09e80a84 100644 --- a/doc/equations/ibeta3.svg +++ b/doc/equations/ibeta3.svg @@ -1,2 +1,2 @@ - + ibeta(a,b,x)=Ix(a,b)=1beta(a,b)∫0xta−1(1−t)b−1dt \ No newline at end of file diff --git a/doc/equations/ibeta4.svg b/doc/equations/ibeta4.svg index f1d9a6b88..c47df905d 100644 --- a/doc/equations/ibeta4.svg +++ b/doc/equations/ibeta4.svg @@ -1,2 +1,2 @@ - + ibetac(a,b,x)=1−Ix(a,b)=I1−x(b,a) \ No newline at end of file diff --git a/doc/equations/ibeta5.svg b/doc/equations/ibeta5.svg index b1c2f2be8..846aa56d4 100644 --- a/doc/equations/ibeta5.svg +++ b/doc/equations/ibeta5.svg @@ -1,2 +1,2 @@ - + Ix(a,b)=xaybaB(a,b)(11+d11+d21+…)d2m+1=−(a+m)(a+b+m)x(a+2m)(a+2m+1)d2m=m(b−m)x(a+2m−1)(a+2m) \ No newline at end of file diff --git a/doc/equations/ibeta6.svg b/doc/equations/ibeta6.svg index b9a933eb8..ea173772d 100644 --- a/doc/equations/ibeta6.svg +++ b/doc/equations/ibeta6.svg @@ -1,2 +1,2 @@ - + Ix(a,b)=xaybB(a,b)(α1β1+α2β2+α3β3+…)α1=1,αm+1=(a+m−1)(a+b+m−1)m(b−m)x2(a+2m−1)2βm+1=m+m(b−m)xa+2m−1+(a+m)(a−(a+b)x+1+m(2−x))a+2m+1 \ No newline at end of file diff --git a/doc/equations/ibeta7.svg b/doc/equations/ibeta7.svg index 93f5af7ab..4bdc191df 100644 --- a/doc/equations/ibeta7.svg +++ b/doc/equations/ibeta7.svg @@ -1,2 +1,2 @@ - + Ix(a,b)=xaB(a,b)∑n=1∞(1−b)n−xn(a+n)n! \ No newline at end of file diff --git a/doc/equations/ibeta8.svg b/doc/equations/ibeta8.svg index ecfe73bea..4b8370d39 100644 --- a/doc/equations/ibeta8.svg +++ b/doc/equations/ibeta8.svg @@ -1,2 +1,2 @@ - + Ix(a,b)≈M∑n=0∞pnJn(b,u);a>bM=H(b,u)Γ(a+b)Γ(a)TbH(c,u)=e−uucΓ(a)T=a+b−12u=−Tln(x)p0=1pn=(b−1)(2n−1)!+1n∑m=1n−1(mb−n)(2m+1)!pn−m \ No newline at end of file diff --git a/doc/equations/ibeta9.svg b/doc/equations/ibeta9.svg index 9ab97fa8c..82f39ce80 100644 --- a/doc/equations/ibeta9.svg +++ b/doc/equations/ibeta9.svg @@ -1,2 +1,2 @@ - + Jn(b,u)=(u2T)2nQ(b+2n,u)H(b+2n,u)=(−lnx2)2nQ(b+2n,u)H(b+2n,u) \ No newline at end of file diff --git a/doc/equations/ibeta_inv1.svg b/doc/equations/ibeta_inv1.svg index 1d5d77e13..abc7b86ba 100644 --- a/doc/equations/ibeta_inv1.svg +++ b/doc/equations/ibeta_inv1.svg @@ -1,2 +1,2 @@ - + Ix−1(a,b)≈(apB(a,b))1a+b−1a+1(apB(a,b))2a+(b−1)(a2+3ba−a+5b−4)2(a+1)2(a+2)(apB(a,b))3a \ No newline at end of file diff --git a/doc/equations/ibeta_inv2.svg b/doc/equations/ibeta_inv2.svg index c9517d47b..8d92aa73d 100644 --- a/doc/equations/ibeta_inv2.svg +++ b/doc/equations/ibeta_inv2.svg @@ -1,2 +1,2 @@ - + Ix(a,a+β);β<a \ No newline at end of file diff --git a/doc/equations/ibeta_inv3.svg b/doc/equations/ibeta_inv3.svg index 6b6a8de57..c4a5a6730 100644 --- a/doc/equations/ibeta_inv3.svg +++ b/doc/equations/ibeta_inv3.svg @@ -1,2 +1,2 @@ - + Ix(a,b);0.2≤aa+b≤0.8 \ No newline at end of file diff --git a/doc/equations/ibeta_inv4.svg b/doc/equations/ibeta_inv4.svg index 1c1b05494..dae1fd68d 100644 --- a/doc/equations/ibeta_inv4.svg +++ b/doc/equations/ibeta_inv4.svg @@ -1,2 +1,2 @@ - + Ix−1(a,b)≈(apB(a,b))1a \ No newline at end of file diff --git a/doc/equations/ibeta_inv5.svg b/doc/equations/ibeta_inv5.svg index d9c81907a..4f908c544 100644 --- a/doc/equations/ibeta_inv5.svg +++ b/doc/equations/ibeta_inv5.svg @@ -1,2 +1,2 @@ - + p=1−q=Ix(a,b)=1−Iy(b,a);y=1−x \ No newline at end of file diff --git a/doc/equations/ibeta_inv6.svg b/doc/equations/ibeta_inv6.svg index 10bd3e23d..d4119d27a 100644 --- a/doc/equations/ibeta_inv6.svg +++ b/doc/equations/ibeta_inv6.svg @@ -1,2 +1,2 @@ - + y=1−Ix−1(a,b)≈(bqB(a,b))1b \ No newline at end of file diff --git a/doc/equations/ibeta_inv7.svg b/doc/equations/ibeta_inv7.svg index c02734af9..6ecfa8830 100644 --- a/doc/equations/ibeta_inv7.svg +++ b/doc/equations/ibeta_inv7.svg @@ -1,2 +1,2 @@ - + x0=xg1+xg;xg=(apB(a,b))1a \ No newline at end of file diff --git a/doc/equations/ibeta_inv8.svg b/doc/equations/ibeta_inv8.svg index 3c6fd126f..ea845d8ba 100644 --- a/doc/equations/ibeta_inv8.svg +++ b/doc/equations/ibeta_inv8.svg @@ -1,2 +1,2 @@ - + y=(1−pbB(a,b))1b \ No newline at end of file diff --git a/doc/equations/igamma1.svg b/doc/equations/igamma1.svg index fb1d1a975..74a50a12e 100644 --- a/doc/equations/igamma1.svg +++ b/doc/equations/igamma1.svg @@ -1,2 +1,2 @@ - + tgamma(a,z)=Γ(a,z)=∫z∞ta−1e−tdt \ No newline at end of file diff --git a/doc/equations/igamma10.svg b/doc/equations/igamma10.svg index 104560b03..10ef06239 100644 --- a/doc/equations/igamma10.svg +++ b/doc/equations/igamma10.svg @@ -1,2 +1,2 @@ - + γ(a,x)=xa∑k=0∞(−1)kxk(a+k)k! \ No newline at end of file diff --git a/doc/equations/igamma11.svg b/doc/equations/igamma11.svg index bfad5d859..407ca8089 100644 --- a/doc/equations/igamma11.svg +++ b/doc/equations/igamma11.svg @@ -1,2 +1,2 @@ - + Γ(a,x)=tgamma1pm1(a)−powm1(x,a)a+xa∑k=1∞(−1)kxk(a+k)k!tgamma1pm1(a)=Γ(a+1)−1powm1(x,a)=xa−1 \ No newline at end of file diff --git a/doc/equations/igamma11b.svg b/doc/equations/igamma11b.svg index 90bb4ec49..447ef00bb 100644 --- a/doc/equations/igamma11b.svg +++ b/doc/equations/igamma11b.svg @@ -1,2 +1,2 @@ - + gp1m1(z)=1+zg+0.5([(z+g−0.5e)z−1]+[L(z)−1](z+g−0.5e)z)+[1+zg+0.5−1] \ No newline at end of file diff --git a/doc/equations/igamma12.svg b/doc/equations/igamma12.svg index 8b6393414..4b8e4b75b 100644 --- a/doc/equations/igamma12.svg +++ b/doc/equations/igamma12.svg @@ -1,2 +1,2 @@ - + xae−xΓ(a)=ex−a(xa+g−0.5)aa+g−0.5e1L(a) \ No newline at end of file diff --git a/doc/equations/igamma13.svg b/doc/equations/igamma13.svg index 597dc67fe..ae792a783 100644 --- a/doc/equations/igamma13.svg +++ b/doc/equations/igamma13.svg @@ -1,2 +1,2 @@ - + ex−a(xa+g−0.5)a=e(alog1pmx(x−a−g+0.5a+g−0.5)+x(0.5−g)a+g−0.5);log1pmx(z)=ln(1+z)−z \ No newline at end of file diff --git a/doc/equations/igamma16.svg b/doc/equations/igamma16.svg index 7f28d9241..77a2a0e95 100644 --- a/doc/equations/igamma16.svg +++ b/doc/equations/igamma16.svg @@ -1,2 +1,2 @@ - + P(a,x)=12erfc(y)−e−y2πaT(a,λ);λ≤1 \ No newline at end of file diff --git a/doc/equations/igamma17.svg b/doc/equations/igamma17.svg index 388cb2161..f1676bcfc 100644 --- a/doc/equations/igamma17.svg +++ b/doc/equations/igamma17.svg @@ -1,2 +1,2 @@ - + Q(a,x)=12erfc(y)+e−y2πaT(a,λ);λ>1 \ No newline at end of file diff --git a/doc/equations/igamma18.svg b/doc/equations/igamma18.svg index 04382789c..83fe5d579 100644 --- a/doc/equations/igamma18.svg +++ b/doc/equations/igamma18.svg @@ -1,2 +1,2 @@ - + λ=xa,y=a(λ−1−lnλ)=−a(ln(1+σ)−σ);σ=x−aa \ No newline at end of file diff --git a/doc/equations/igamma19.svg b/doc/equations/igamma19.svg index b255960a0..86edf9ef7 100644 --- a/doc/equations/igamma19.svg +++ b/doc/equations/igamma19.svg @@ -1,2 +1,2 @@ - + T(a,λ)=∑k=0N(∑n=0MCknzn)a−k;z=sign(λ−1)2σ \ No newline at end of file diff --git a/doc/equations/igamma1f.svg b/doc/equations/igamma1f.svg index 4516fdaa5..87ae3ae0d 100644 --- a/doc/equations/igamma1f.svg +++ b/doc/equations/igamma1f.svg @@ -1,2 +1,2 @@ - + Q(a,x)=e−x∑n=0a−1xnn!;a∈ℕ+ \ No newline at end of file diff --git a/doc/equations/igamma2.svg b/doc/equations/igamma2.svg index e064cddf1..1c2b976e6 100644 --- a/doc/equations/igamma2.svg +++ b/doc/equations/igamma2.svg @@ -1,2 +1,2 @@ - + tgamma_lower(a,z)=γ(a,z)=∫0zta−1e−tdt \ No newline at end of file diff --git a/doc/equations/igamma2f.svg b/doc/equations/igamma2f.svg index 971e7cb9e..80f927aff 100644 --- a/doc/equations/igamma2f.svg +++ b/doc/equations/igamma2f.svg @@ -1,2 +1,2 @@ - + Q(a,x)=erfc(x)+e−xπx∑n=1ixn(1−12)…(n−12);a=i+12;i∈ℕ+ \ No newline at end of file diff --git a/doc/equations/igamma3.svg b/doc/equations/igamma3.svg index 6e240199e..6cf729441 100644 --- a/doc/equations/igamma3.svg +++ b/doc/equations/igamma3.svg @@ -1,2 +1,2 @@ - + gamma_q(a,z)=Q(a,z)=Γ(a,z)Γ(a)=1Γ(a)∫z∞ta−1e−tdt \ No newline at end of file diff --git a/doc/equations/igamma4.svg b/doc/equations/igamma4.svg index ac0f9d2d3..d5f54d1ac 100644 --- a/doc/equations/igamma4.svg +++ b/doc/equations/igamma4.svg @@ -1,2 +1,2 @@ - + gamma_p(a,z)=P(a,z)=γ(a,z)Γ(a)=1Γ(a)∫0zta−1e−tdt \ No newline at end of file diff --git a/doc/equations/igamma5.svg b/doc/equations/igamma5.svg index 820f9eba4..2c51fb503 100644 --- a/doc/equations/igamma5.svg +++ b/doc/equations/igamma5.svg @@ -1,2 +1,2 @@ - + Q(a,x)+P(a,x)=1 \ No newline at end of file diff --git a/doc/equations/igamma6.svg b/doc/equations/igamma6.svg index aed303bc8..84c2845b4 100644 --- a/doc/equations/igamma6.svg +++ b/doc/equations/igamma6.svg @@ -1,2 +1,2 @@ - + Γ(a,z)+γ(a,z)=Γ(a) \ No newline at end of file diff --git a/doc/equations/igamma7.svg b/doc/equations/igamma7.svg index fd2f4ba78..b833b3646 100644 --- a/doc/equations/igamma7.svg +++ b/doc/equations/igamma7.svg @@ -1,2 +1,2 @@ - + Q(a,z)=Γ(a,z)Γ(a),P(a,z)=γ(a,z)Γ(a) \ No newline at end of file diff --git a/doc/equations/igamma8.svg b/doc/equations/igamma8.svg index aab96f886..be6b0b261 100644 --- a/doc/equations/igamma8.svg +++ b/doc/equations/igamma8.svg @@ -1,2 +1,2 @@ - + γ(a,x)=xae−x∑k=0∞Γ(a)Γ(a+k+1)xn=xae−x∑k=0∞xnak+1− \ No newline at end of file diff --git a/doc/equations/igamma9.svg b/doc/equations/igamma9.svg index 3f5623f1a..9f5cd0e0a 100644 --- a/doc/equations/igamma9.svg +++ b/doc/equations/igamma9.svg @@ -1,2 +1,2 @@ - + Γ(a,x)=xae−xx−a+1+akbk+ak+1bk+1+…;ak=k(a−k);bk=x−a+2k+1 \ No newline at end of file diff --git a/doc/equations/jacobi1.svg b/doc/equations/jacobi1.svg index b18fc9313..0c00def4e 100644 --- a/doc/equations/jacobi1.svg +++ b/doc/equations/jacobi1.svg @@ -1,2 +1,2 @@ - + u=∫0φdφ(1−k2sin2φ) \ No newline at end of file diff --git a/doc/equations/jacobi2.svg b/doc/equations/jacobi2.svg index 00aa8a21a..821472fa7 100644 --- a/doc/equations/jacobi2.svg +++ b/doc/equations/jacobi2.svg @@ -1,2 +1,2 @@ - + sn(u,k)=sinφcn(u,k)=cosφdn(u,k)=(1−k2sin2φ) \ No newline at end of file diff --git a/doc/equations/jacobi3.svg b/doc/equations/jacobi3.svg index 6364d08aa..288dad8f9 100644 --- a/doc/equations/jacobi3.svg +++ b/doc/equations/jacobi3.svg @@ -1,2 +1,2 @@ - + μ=1k2ν=uksn(u,k)=sn(ν,μ)kcn(u,k)=dn(ν,μ)dn(u,k)=cn(ν,k) \ No newline at end of file diff --git a/doc/equations/jacobi4.svg b/doc/equations/jacobi4.svg index 923088789..9d6cef34a 100644 --- a/doc/equations/jacobi4.svg +++ b/doc/equations/jacobi4.svg @@ -1,2 +1,2 @@ - + sn(u,k)≈sin(u)−14k2(u−sin(u)cos(u))cos(u)cn(u,k)≈cos(u)+14k2(u−sin(u)cos(u))sin(u)dn(u,k)≈1−12k2sin2(u) \ No newline at end of file diff --git a/doc/equations/laguerre_0.svg b/doc/equations/laguerre_0.svg index c8491b32d..e07421957 100644 --- a/doc/equations/laguerre_0.svg +++ b/doc/equations/laguerre_0.svg @@ -1,2 +1,2 @@ - + laguerre(n,x)=Ln(x)=exn!dndxn(xne−x) \ No newline at end of file diff --git a/doc/equations/laguerre_1.svg b/doc/equations/laguerre_1.svg index 37a836bf7..3e6212b64 100644 --- a/doc/equations/laguerre_1.svg +++ b/doc/equations/laguerre_1.svg @@ -1,2 +1,2 @@ - + laguerre(n,m,x)=Lnm(x)=(−1)mdmdxmLn+m(x) \ No newline at end of file diff --git a/doc/equations/laguerre_2.svg b/doc/equations/laguerre_2.svg index 803154087..d8f45761e 100644 --- a/doc/equations/laguerre_2.svg +++ b/doc/equations/laguerre_2.svg @@ -1,2 +1,2 @@ - + Ln+1(x)=(2n+1−x)Ln(x)−nLn−1(x)(n+1) \ No newline at end of file diff --git a/doc/equations/laguerre_3.svg b/doc/equations/laguerre_3.svg index d7c5a7d26..a414bb78a 100644 --- a/doc/equations/laguerre_3.svg +++ b/doc/equations/laguerre_3.svg @@ -1,2 +1,2 @@ - + Ln+1m(x)=m+2n+1−xn+1Lnm(x)−m+nn+1Ln−1m(x) \ No newline at end of file diff --git a/doc/equations/lanczos0.svg b/doc/equations/lanczos0.svg index 9c3f6598b..1d6615cde 100644 --- a/doc/equations/lanczos0.svg +++ b/doc/equations/lanczos0.svg @@ -1,2 +1,2 @@ - + Γ(z+1)=2π(z+g+0.5)z+0.5e−(z+g+0.5)Sg(z) \ No newline at end of file diff --git a/doc/equations/lanczos0a.svg b/doc/equations/lanczos0a.svg index cace8cd62..c2c872d78 100644 --- a/doc/equations/lanczos0a.svg +++ b/doc/equations/lanczos0a.svg @@ -1,2 +1,2 @@ - + Sg(z)=[12a0+a1zz+1+a2z(z−1)(z+1)(z+2)+…] \ No newline at end of file diff --git a/doc/equations/lanczos0b.svg b/doc/equations/lanczos0b.svg index cc5ee593a..aeea964ba 100644 --- a/doc/equations/lanczos0b.svg +++ b/doc/equations/lanczos0b.svg @@ -1,2 +1,2 @@ - + ak=(−1)k2πegk∑j=0k(−1)j(k+j−1)!(k−j)!j!(ej+g+12)j+12 \ No newline at end of file diff --git a/doc/equations/lanczos1.svg b/doc/equations/lanczos1.svg index 9f85ae72f..760e41434 100644 --- a/doc/equations/lanczos1.svg +++ b/doc/equations/lanczos1.svg @@ -1,2 +1,2 @@ - + Γ(z)=(z+g−0.5)z−0.5ez+g−0.5Lg(z); \ No newline at end of file diff --git a/doc/equations/lanczos2.svg b/doc/equations/lanczos2.svg index fe346dacf..66f9221b1 100644 --- a/doc/equations/lanczos2.svg +++ b/doc/equations/lanczos2.svg @@ -1,2 +1,2 @@ - + Lg(z)=C0+∑k=1N−1CNz+k−1 \ No newline at end of file diff --git a/doc/equations/lanczos3.svg b/doc/equations/lanczos3.svg index 402d143ee..7583266b7 100644 --- a/doc/equations/lanczos3.svg +++ b/doc/equations/lanczos3.svg @@ -1,2 +1,2 @@ - + Dij={0ifi≠j1ifi=j=0−1ifi=j=1Di−1,i−12(2i−1)i−1otherwise \ No newline at end of file diff --git a/doc/equations/lanczos4.svg b/doc/equations/lanczos4.svg index af79befee..08c6bc14e 100644 --- a/doc/equations/lanczos4.svg +++ b/doc/equations/lanczos4.svg @@ -1,2 +1,2 @@ - + Bi,j={1ifi=0−1j−iXifi>0j≥i0otherwise;X=(i+j−1j−i) \ No newline at end of file diff --git a/doc/equations/lanczos5.svg b/doc/equations/lanczos5.svg index 3d817cfac..65c587d0e 100644 --- a/doc/equations/lanczos5.svg +++ b/doc/equations/lanczos5.svg @@ -1,2 +1,2 @@ - + Ci,j={12ifi=j=00ifj>i−1i−jSotherwise;S=∑k=0i(2i2k)(kk+j−i) \ No newline at end of file diff --git a/doc/equations/lanczos6.svg b/doc/equations/lanczos6.svg index 47674c0dd..842cd3de6 100644 --- a/doc/equations/lanczos6.svg +++ b/doc/equations/lanczos6.svg @@ -1,2 +1,2 @@ - + Fi=(2i)!ei+g+0.5i!22i−1(i+g+0.5)i+0.5 \ No newline at end of file diff --git a/doc/equations/lanczos7.svg b/doc/equations/lanczos7.svg index c5c47eeb5..dd877839e 100644 --- a/doc/equations/lanczos7.svg +++ b/doc/equations/lanczos7.svg @@ -1,2 +1,2 @@ - + Γ(z)=(z+g−0.5e)z−0.5Lg,e(z); \ No newline at end of file diff --git a/doc/equations/laplace_pdf.svg b/doc/equations/laplace_pdf.svg index 579645acb..10cb5d098 100644 --- a/doc/equations/laplace_pdf.svg +++ b/doc/equations/laplace_pdf.svg @@ -1,2 +1,2 @@ - + f(x;μ,σ)=12σe−|x−μ|σ \ No newline at end of file diff --git a/doc/equations/legendre_0.svg b/doc/equations/legendre_0.svg index 89f6fb14e..5b2e572a6 100644 --- a/doc/equations/legendre_0.svg +++ b/doc/equations/legendre_0.svg @@ -1,2 +1,2 @@ - + legendre_p(l,x)=Pl(x)=12ll!dldxl(x2−1)l;|x|≤1 \ No newline at end of file diff --git a/doc/equations/legendre_1.svg b/doc/equations/legendre_1.svg index 0d7443961..02c4b3905 100644 --- a/doc/equations/legendre_1.svg +++ b/doc/equations/legendre_1.svg @@ -1,2 +1,2 @@ - + legendre_p(l,m,x)=Plm(x)=(−1)m(1−x2)m2dmPl(x)dxm \ No newline at end of file diff --git a/doc/equations/legendre_1b.svg b/doc/equations/legendre_1b.svg index 34bb271d7..bce46ba26 100644 --- a/doc/equations/legendre_1b.svg +++ b/doc/equations/legendre_1b.svg @@ -1,2 +1,2 @@ - + legendre_p(l,m,x)=Plm(x)=(1−x2)m2dmPl(x)dxm \ No newline at end of file diff --git a/doc/equations/legendre_2.svg b/doc/equations/legendre_2.svg index cd5965421..3cacc8cb0 100644 --- a/doc/equations/legendre_2.svg +++ b/doc/equations/legendre_2.svg @@ -1,2 +1,2 @@ - + legendre_q(0,x)=Q0(x)=12ln(1+x1−x)legendre_q(1,x)=Q1(x)=x2ln(1+x1−x)−1 \ No newline at end of file diff --git a/doc/equations/legendre_3.svg b/doc/equations/legendre_3.svg index 82ccc6c46..62e20a799 100644 --- a/doc/equations/legendre_3.svg +++ b/doc/equations/legendre_3.svg @@ -1,2 +1,2 @@ - + Pl−m(x)=(−1)m(l−m)!(l+m)!Plm(x)P−l−1m(x)=Plm(x) \ No newline at end of file diff --git a/doc/equations/legendre_4.svg b/doc/equations/legendre_4.svg index f238ebbd3..a108b7fe0 100644 --- a/doc/equations/legendre_4.svg +++ b/doc/equations/legendre_4.svg @@ -1,2 +1,2 @@ - + Pl+1(x)=(2l+1)xPl(x)−lPl−1(x)(l+1) \ No newline at end of file diff --git a/doc/equations/legendre_5.svg b/doc/equations/legendre_5.svg index d31e4d13d..f09c13c90 100644 --- a/doc/equations/legendre_5.svg +++ b/doc/equations/legendre_5.svg @@ -1,2 +1,2 @@ - + Pl+1m(x)=(2l+1)xPlm(x)−(l+m+1)Pl−1m(x)(l−m+1) \ No newline at end of file diff --git a/doc/equations/lgamm1.svg b/doc/equations/lgamm1.svg index bc879a8af..cd9930f1c 100644 --- a/doc/equations/lgamm1.svg +++ b/doc/equations/lgamm1.svg @@ -1,2 +1,2 @@ - + lgamma(z)=ln|Γ(z)| \ No newline at end of file diff --git a/doc/equations/lgamm2.svg b/doc/equations/lgamm2.svg index 6d272808a..825605451 100644 --- a/doc/equations/lgamm2.svg +++ b/doc/equations/lgamm2.svg @@ -1,2 +1,2 @@ - + ln(|Γ(z)|)=zln(l)−l+ln(∑0∞lnzn−+1z−c1d1+c2d2+c3d3+…);ck=−(z+k−1)∧dk=z+k+l \ No newline at end of file diff --git a/doc/equations/lgamm3.svg b/doc/equations/lgamm3.svg index eb9cf4322..13172bad6 100644 --- a/doc/equations/lgamm3.svg +++ b/doc/equations/lgamm3.svg @@ -1,2 +1,2 @@ - + ln(|Γ(−z)|)=ln(π)−ln(Γ(z))−ln(zsin(πz)) \ No newline at end of file diff --git a/doc/equations/lgamm4.svg b/doc/equations/lgamm4.svg index d15e370ca..611f6d71a 100644 --- a/doc/equations/lgamm4.svg +++ b/doc/equations/lgamm4.svg @@ -1,2 +1,2 @@ - + ln(|Γ(z)|)=(z−0.5)ln(z+g−0.5e)+ln(Le,g(z)) \ No newline at end of file diff --git a/doc/equations/lgamm5.svg b/doc/equations/lgamm5.svg index 1ddc05c72..781ace303 100644 --- a/doc/equations/lgamm5.svg +++ b/doc/equations/lgamm5.svg @@ -1,2 +1,2 @@ - + ln(|Γ(z)|)=Δzln(Δz+g+0.5e)+12ln(1+Δzg+0.5)+ln(1+∑k=0N−1Δzdkk(Δz+k))Δz=1−z∧dk=g+0.5e(Ckeg) \ No newline at end of file diff --git a/doc/equations/lgamm6.svg b/doc/equations/lgamm6.svg index 7a1e34479..fca3d28b7 100644 --- a/doc/equations/lgamm6.svg +++ b/doc/equations/lgamm6.svg @@ -1,2 +1,2 @@ - + ln(|Γ(z)|)=32ln(1+Δzg+1.5)+Δzln(z+g−0.5e)+ln(1+∑k=1N−1−dkΔzz+kz+k2−1)Δz=z−2∧dk=(g+1.5e)1.5(Ckeg) \ No newline at end of file diff --git a/doc/equations/log1pseries.svg b/doc/equations/log1pseries.svg index 1d2ee5cc9..d9bde2883 100644 --- a/doc/equations/log1pseries.svg +++ b/doc/equations/log1pseries.svg @@ -1,2 +1,2 @@ - + log(1+x)=∑k=1∞(−1)k−1xkk \ No newline at end of file diff --git a/doc/equations/lognormal_ref.svg b/doc/equations/lognormal_ref.svg index 8e418c9d2..5e038d0f8 100644 --- a/doc/equations/lognormal_ref.svg +++ b/doc/equations/lognormal_ref.svg @@ -1,2 +1,2 @@ - + f(x)=1xs2πe−(lnx−m)22s2 \ No newline at end of file diff --git a/doc/equations/mbessel1.svg b/doc/equations/mbessel1.svg index e37f4146a..681a30ded 100644 --- a/doc/equations/mbessel1.svg +++ b/doc/equations/mbessel1.svg @@ -1,2 +1,2 @@ - + z2d2udz2+zdudz−(z2+ν2)u=0 \ No newline at end of file diff --git a/doc/equations/mbessel10.svg b/doc/equations/mbessel10.svg index 538f156da..b97d70cf7 100644 --- a/doc/equations/mbessel10.svg +++ b/doc/equations/mbessel10.svg @@ -1,2 +1,2 @@ - + K−ν(z)=Kν(z) \ No newline at end of file diff --git a/doc/equations/mbessel11.svg b/doc/equations/mbessel11.svg index 20ca9bb4a..52ec4f77b 100644 --- a/doc/equations/mbessel11.svg +++ b/doc/equations/mbessel11.svg @@ -1,2 +1,2 @@ - + CF1:fν=Iν+1Iν=12(ν+1)x+12(ν+2)x+⋅⋅⋅ \ No newline at end of file diff --git a/doc/equations/mbessel12.svg b/doc/equations/mbessel12.svg index 37c92f917..7425522a3 100644 --- a/doc/equations/mbessel12.svg +++ b/doc/equations/mbessel12.svg @@ -1,2 +1,2 @@ - + CF2:z1z0=12(x+1)+ν2−(32)22(x+2)+ν2−(52)22(x+3)+⋅⋅⋅ \ No newline at end of file diff --git a/doc/equations/mbessel13.svg b/doc/equations/mbessel13.svg index d4cee6952..d602aeef0 100644 --- a/doc/equations/mbessel13.svg +++ b/doc/equations/mbessel13.svg @@ -1,2 +1,2 @@ - + Kμ=π(2x)μe−xz0Kμ+1=Kμx[12+μ+x+(μ2−14)z1z0] \ No newline at end of file diff --git a/doc/equations/mbessel14.svg b/doc/equations/mbessel14.svg index 75554f277..3650caf96 100644 --- a/doc/equations/mbessel14.svg +++ b/doc/equations/mbessel14.svg @@ -1,2 +1,2 @@ - + z0=11+S(12x)μ+12 \ No newline at end of file diff --git a/doc/equations/mbessel15.svg b/doc/equations/mbessel15.svg index 01f0cd22f..4fff6dd8b 100644 --- a/doc/equations/mbessel15.svg +++ b/doc/equations/mbessel15.svg @@ -1,2 +1,2 @@ - + Kμ=∑k=0∞ckfkKμ+1=2x∑k=0∞ckhk \ No newline at end of file diff --git a/doc/equations/mbessel16.svg b/doc/equations/mbessel16.svg index 7a7038da7..fcf6d3d56 100644 --- a/doc/equations/mbessel16.svg +++ b/doc/equations/mbessel16.svg @@ -1,2 +1,2 @@ - + ck=1k!(x24)k \ No newline at end of file diff --git a/doc/equations/mbessel17.svg b/doc/equations/mbessel17.svg index d4bf98976..9475b81c9 100644 --- a/doc/equations/mbessel17.svg +++ b/doc/equations/mbessel17.svg @@ -1,2 +1,2 @@ - -Iv(x)=∑k=0∞1Γ(k+v+1)k!(x2)2k+v + +Iv(x)=∑k=0∞1Γ(k+v+1)k!(x2)2k+v diff --git a/doc/equations/mbessel2.svg b/doc/equations/mbessel2.svg index feb9158c3..e73e575d7 100644 --- a/doc/equations/mbessel2.svg +++ b/doc/equations/mbessel2.svg @@ -1,2 +1,2 @@ - + Iν(z)=(12z)ν∑k=0∞(14z2)kk!Γ(ν+k+1) \ No newline at end of file diff --git a/doc/equations/mbessel3.svg b/doc/equations/mbessel3.svg index 44dee3ba9..6c654969d 100644 --- a/doc/equations/mbessel3.svg +++ b/doc/equations/mbessel3.svg @@ -1,2 +1,2 @@ - + Kν(z)=π2⋅I−ν(z)−Iν(z)sin(νπ) \ No newline at end of file diff --git a/doc/equations/mbessel4.svg b/doc/equations/mbessel4.svg index 7e51b8247..f17df11df 100644 --- a/doc/equations/mbessel4.svg +++ b/doc/equations/mbessel4.svg @@ -1,2 +1,2 @@ - + Iν+1(z)=−2νzIν(z)+Iν−1(z) \ No newline at end of file diff --git a/doc/equations/mbessel5.svg b/doc/equations/mbessel5.svg index 670f663a3..5227fd73e 100644 --- a/doc/equations/mbessel5.svg +++ b/doc/equations/mbessel5.svg @@ -1,2 +1,2 @@ - + Kν+1(z)=2νzKν(z)+Kν−1(z) \ No newline at end of file diff --git a/doc/equations/mbessel6.svg b/doc/equations/mbessel6.svg index 432a651bb..76b904e19 100644 --- a/doc/equations/mbessel6.svg +++ b/doc/equations/mbessel6.svg @@ -1,2 +1,2 @@ - + Iν′(z)=νzIν(z)+Iν+1(z) \ No newline at end of file diff --git a/doc/equations/mbessel7.svg b/doc/equations/mbessel7.svg index dea9d5118..32d449d18 100644 --- a/doc/equations/mbessel7.svg +++ b/doc/equations/mbessel7.svg @@ -1,2 +1,2 @@ - + Kν′(z)=νzKν(z)−Kν+1(z) \ No newline at end of file diff --git a/doc/equations/mbessel8.svg b/doc/equations/mbessel8.svg index 20203189f..d53d54194 100644 --- a/doc/equations/mbessel8.svg +++ b/doc/equations/mbessel8.svg @@ -1,2 +1,2 @@ - + W=Iν(z)Kν′(z)−Kν(z)Iν′(z)=−[Iν(z)Kν+1(z)+Kν(z)Iν+1(z)]=−1z \ No newline at end of file diff --git a/doc/equations/mbessel9.svg b/doc/equations/mbessel9.svg index 8fc21946e..b1a444fdc 100644 --- a/doc/equations/mbessel9.svg +++ b/doc/equations/mbessel9.svg @@ -1,2 +1,2 @@ - + I−ν(z)=Iν(z)+2πsin(νπ)Kν(z) \ No newline at end of file diff --git a/doc/equations/nc_beta_ref1.svg b/doc/equations/nc_beta_ref1.svg index 1703e6881..1c79e475c 100644 --- a/doc/equations/nc_beta_ref1.svg +++ b/doc/equations/nc_beta_ref1.svg @@ -1,2 +1,2 @@ - + f(x;α,β;λ)=∑i=0∞P(i;λ2)Ix′(α+i,β) \ No newline at end of file diff --git a/doc/equations/nc_beta_ref2.svg b/doc/equations/nc_beta_ref2.svg index baad52030..23641a94e 100644 --- a/doc/equations/nc_beta_ref2.svg +++ b/doc/equations/nc_beta_ref2.svg @@ -1,2 +1,2 @@ - + F(x;α,β;λ)=∑i=0∞P(i;λ2)Ix(α+i,β) \ No newline at end of file diff --git a/doc/equations/nc_beta_ref3.svg b/doc/equations/nc_beta_ref3.svg index 99834b203..cc58fc5d2 100644 --- a/doc/equations/nc_beta_ref3.svg +++ b/doc/equations/nc_beta_ref3.svg @@ -1,2 +1,2 @@ - + E(X)≃1−(βC)(1+λ2C2);C=α+β+λ2 \ No newline at end of file diff --git a/doc/equations/nc_beta_ref4.svg b/doc/equations/nc_beta_ref4.svg index 8fbf8f495..d2da9269a 100644 --- a/doc/equations/nc_beta_ref4.svg +++ b/doc/equations/nc_beta_ref4.svg @@ -1,2 +1,2 @@ - + F(x;α,β;λ)=∑i=0∞P(i;λ2)Ix(α+i,β)1−F(x;α,β;λ)=∑i=0∞P(i;λ2)(1−Ix(α+i,β)) \ No newline at end of file diff --git a/doc/equations/nc_chi_squ_ref1.svg b/doc/equations/nc_chi_squ_ref1.svg index 13d5d9dd0..2be1c0b8e 100644 --- a/doc/equations/nc_chi_squ_ref1.svg +++ b/doc/equations/nc_chi_squ_ref1.svg @@ -1,2 +1,2 @@ - + ∑i=1k(χiσi)2 \ No newline at end of file diff --git a/doc/equations/nc_chi_squ_ref2.svg b/doc/equations/nc_chi_squ_ref2.svg index ee068fcf7..5da2c58bb 100644 --- a/doc/equations/nc_chi_squ_ref2.svg +++ b/doc/equations/nc_chi_squ_ref2.svg @@ -1,2 +1,2 @@ - + λ=∑i=1k(μiσi)2 \ No newline at end of file diff --git a/doc/equations/nc_chi_squ_ref3.svg b/doc/equations/nc_chi_squ_ref3.svg index 0cf0c9ad2..db53746e3 100644 --- a/doc/equations/nc_chi_squ_ref3.svg +++ b/doc/equations/nc_chi_squ_ref3.svg @@ -1,2 +1,2 @@ - + f(x;ν,λ)=∑i=0∞e(−λ2)(λ2)ii!f(x;ν+2i)=12e[−(x+λ)2](xλ)(ν4−12)I(k2−1)(λx) \ No newline at end of file diff --git a/doc/equations/nc_chi_squ_ref4.svg b/doc/equations/nc_chi_squ_ref4.svg index b5aa0d5fc..377a8331b 100644 --- a/doc/equations/nc_chi_squ_ref4.svg +++ b/doc/equations/nc_chi_squ_ref4.svg @@ -1,2 +1,2 @@ - + P(x;ν,λ)=∑i=0∞sitis0=u0=e−λ2,si=si−1+ui,ui=ui−1λ2it0=1Γ(ν2+1)(x2)ν2e−x2,ti=ti−1xν+2i \ No newline at end of file diff --git a/doc/equations/nc_chi_squ_ref5.svg b/doc/equations/nc_chi_squ_ref5.svg index 4d77d00e8..ef7695ea3 100644 --- a/doc/equations/nc_chi_squ_ref5.svg +++ b/doc/equations/nc_chi_squ_ref5.svg @@ -1,2 +1,2 @@ - + P(x;ν,λ)=∑i=0∞e−λ2(λ2)ii!Px2(ν2+i) \ No newline at end of file diff --git a/doc/equations/nc_chi_squ_ref6.svg b/doc/equations/nc_chi_squ_ref6.svg index 4b0441d79..e82cf9c81 100644 --- a/doc/equations/nc_chi_squ_ref6.svg +++ b/doc/equations/nc_chi_squ_ref6.svg @@ -1,2 +1,2 @@ - + 1−P(x;ν,λ)=∑i=0∞e−λ2(λ2)ii!Qx2(ν2+i) \ No newline at end of file diff --git a/doc/equations/nc_chi_squ_ref7.svg b/doc/equations/nc_chi_squ_ref7.svg index 9d80b55fb..d5f25d8bd 100644 --- a/doc/equations/nc_chi_squ_ref7.svg +++ b/doc/equations/nc_chi_squ_ref7.svg @@ -1,2 +1,2 @@ - + mean=ν+λvariance=2(ν+2λ)skewness=232(ν+3λ)(ν+2λ)32 \ No newline at end of file diff --git a/doc/equations/nc_f_ref1.svg b/doc/equations/nc_f_ref1.svg index c08ee1c3e..bcffa33e5 100644 --- a/doc/equations/nc_f_ref1.svg +++ b/doc/equations/nc_f_ref1.svg @@ -1,2 +1,2 @@ - + f(x;ν1,ν2;λ)=e−λ2+(λν1x)(2(ν2+ν1x))ν1ν12ν2ν22xν12−1(ν2+ν1x)−(ν1+ν2)2Γ(12ν1)Γ(1+12ν2)Lν22ν12−1(−λν1x2(ν2+ν1x))B(12ν1,12ν2)Γ(12(ν1+ν2)) \ No newline at end of file diff --git a/doc/equations/nc_f_ref2.svg b/doc/equations/nc_f_ref2.svg index 858a225a8..74a4926cf 100644 --- a/doc/equations/nc_f_ref2.svg +++ b/doc/equations/nc_f_ref2.svg @@ -1,2 +1,2 @@ - + f(x;ν1,ν2;λ)=∑k=0∞e−λ2(λ2)kB(ν22,ν12+k)k!(ν1ν2)(ν12+k)(ν2ν2+ν1x)(ν1+ν22+k)x(ν12+k−1) \ No newline at end of file diff --git a/doc/equations/nc_t_ref1.svg b/doc/equations/nc_t_ref1.svg index 6bacca1ca..60904c8cc 100644 --- a/doc/equations/nc_t_ref1.svg +++ b/doc/equations/nc_t_ref1.svg @@ -1,2 +1,2 @@ - + f(x;ν;δ)=νν2ν!2νeδ22(ν+x2)ν2Γ(ν2)(2δx1F1(n2+1;32;δ2x22(n+x2))(ν+x2)Γ(12(ν+1))+1F1(12(n+1);12;δ2x22(ν+x2))ν+x2Γ(ν2+1)) \ No newline at end of file diff --git a/doc/equations/nc_t_ref2.svg b/doc/equations/nc_t_ref2.svg index 61b67c34c..3514ef07b 100644 --- a/doc/equations/nc_t_ref2.svg +++ b/doc/equations/nc_t_ref2.svg @@ -1,2 +1,2 @@ - + P(t;ν;δ)=Φ(−δ)+12∑i=0∞(PiIx(i+12,ν2)+δ2QiIx(i+1,ν2))Pi=e−δ22(δ22)ii!,Qi=e−δ22(δ22)iΓ(i+32),x=t2(ν+t2) \ No newline at end of file diff --git a/doc/equations/nc_t_ref3.svg b/doc/equations/nc_t_ref3.svg index da88ffe5f..4ceaf8e17 100644 --- a/doc/equations/nc_t_ref3.svg +++ b/doc/equations/nc_t_ref3.svg @@ -1,2 +1,2 @@ - + P(∞;ν;δ)=1=Φ(−δ)+12∑i=0∞(Pi+δ2Qi) \ No newline at end of file diff --git a/doc/equations/nc_t_ref4.svg b/doc/equations/nc_t_ref4.svg index b41cd324f..c8da7c575 100644 --- a/doc/equations/nc_t_ref4.svg +++ b/doc/equations/nc_t_ref4.svg @@ -1,2 +1,2 @@ - + 1−P(t;ν;δ)=12∑i=0∞(PiIy(ν2,i+12)+δ2QiIy(ν2,i+1));y=1−x=νν+t2 \ No newline at end of file diff --git a/doc/equations/nc_t_ref5.svg b/doc/equations/nc_t_ref5.svg index 3500ff7f3..27160be60 100644 --- a/doc/equations/nc_t_ref5.svg +++ b/doc/equations/nc_t_ref5.svg @@ -1,2 +1,2 @@ - + f(t;ν;δ)=νtν2+2νt2+t4∑i=0∞(PiIx′(i+12,ν2)+δ2QiIx′(i+1,ν2)) \ No newline at end of file diff --git a/doc/equations/neg_binomial_ref.svg b/doc/equations/neg_binomial_ref.svg index 4def4af81..e619c3b81 100644 --- a/doc/equations/neg_binomial_ref.svg +++ b/doc/equations/neg_binomial_ref.svg @@ -1,2 +1,2 @@ - + f(k;r,p)=Γ(r+k)k!Γ(r)pr(1−p)k \ No newline at end of file diff --git a/doc/equations/normal_ref1.svg b/doc/equations/normal_ref1.svg index 1cdf9669d..a3a664abb 100644 --- a/doc/equations/normal_ref1.svg +++ b/doc/equations/normal_ref1.svg @@ -1,2 +1,2 @@ - + f(x;μ,σ)=1σ2πe−(x−μ)22σ2 \ No newline at end of file diff --git a/doc/equations/poisson_ref1.svg b/doc/equations/poisson_ref1.svg index 0f09897ec..4864adc02 100644 --- a/doc/equations/poisson_ref1.svg +++ b/doc/equations/poisson_ref1.svg @@ -1,2 +1,2 @@ - + f(k;λ)=e−λλkk! \ No newline at end of file diff --git a/doc/equations/roots1.svg b/doc/equations/roots1.svg index 9a5989c6d..5195ecdc1 100644 --- a/doc/equations/roots1.svg +++ b/doc/equations/roots1.svg @@ -1,2 +1,2 @@ - + xN+1=xN−f(x)f′(x) \ No newline at end of file diff --git a/doc/equations/roots2.svg b/doc/equations/roots2.svg index 4c7157895..030edfa20 100644 --- a/doc/equations/roots2.svg +++ b/doc/equations/roots2.svg @@ -1,2 +1,2 @@ - + xN+1=xN−2f(x)f′(x)2(f′(x))2−f(x)f″(x) \ No newline at end of file diff --git a/doc/equations/roots3.svg b/doc/equations/roots3.svg index 84eaa5965..b58d8ddbe 100644 --- a/doc/equations/roots3.svg +++ b/doc/equations/roots3.svg @@ -1,2 +1,2 @@ - + xN+1=xN−f(x)f′(x)−f″(x)(f(x))22(f′(x))3 \ No newline at end of file diff --git a/doc/equations/roots4.svg b/doc/equations/roots4.svg index 27e8d52a1..5a39a345d 100644 --- a/doc/equations/roots4.svg +++ b/doc/equations/roots4.svg @@ -1,2 +1,2 @@ - + f(x)=x3−af′(x)=3x2f″(x)=6x \ No newline at end of file diff --git a/doc/equations/sbessel1.svg b/doc/equations/sbessel1.svg index 3c282a2dd..c754ed2a6 100644 --- a/doc/equations/sbessel1.svg +++ b/doc/equations/sbessel1.svg @@ -1,2 +1,2 @@ - + z2d2udz2+2zdudz+[z2−n(n+1)]u=0 \ No newline at end of file diff --git a/doc/equations/sbessel2.svg b/doc/equations/sbessel2.svg index f90d9ac73..6b065f799 100644 --- a/doc/equations/sbessel2.svg +++ b/doc/equations/sbessel2.svg @@ -1,2 +1,2 @@ - + jn(z)=π2zJn+12(z)yn(z)=π2zYn+12(z) \ No newline at end of file diff --git a/doc/equations/sbessel3.svg b/doc/equations/sbessel3.svg index 49ddd3325..fead3edeb 100644 --- a/doc/equations/sbessel3.svg +++ b/doc/equations/sbessel3.svg @@ -1,2 +1,2 @@ - + z2d2udz2+2zdudz−[z2+n(n+1)]u=0 \ No newline at end of file diff --git a/doc/equations/sbessel4.svg b/doc/equations/sbessel4.svg index 5c5679341..10bf040b0 100644 --- a/doc/equations/sbessel4.svg +++ b/doc/equations/sbessel4.svg @@ -1,2 +1,2 @@ - + in(z)=π2zIn+12(z)kn(z)=π2zKn+12(z) \ No newline at end of file diff --git a/doc/equations/sbessel5.svg b/doc/equations/sbessel5.svg index 801c51c83..6656379f7 100644 --- a/doc/equations/sbessel5.svg +++ b/doc/equations/sbessel5.svg @@ -1,2 +1,2 @@ - + jν(z)=π4∑k=0∞(−1)k(z2)2k+nk!Γ(n+k+1+12) \ No newline at end of file diff --git a/doc/equations/special_functions_blurb1.svg b/doc/equations/special_functions_blurb1.svg index 48e9ae251..1765ac230 100644 --- a/doc/equations/special_functions_blurb1.svg +++ b/doc/equations/special_functions_blurb1.svg @@ -1,2 +1,2 @@ - + exp(x)=∑n=0∞xnn! \ No newline at end of file diff --git a/doc/equations/special_functions_blurb15.svg b/doc/equations/special_functions_blurb15.svg index 56b021f76..9e86924ad 100644 --- a/doc/equations/special_functions_blurb15.svg +++ b/doc/equations/special_functions_blurb15.svg @@ -1,2 +1,2 @@ - + atanh(x)=log(1+x1−x)2 \ No newline at end of file diff --git a/doc/equations/special_functions_blurb17.svg b/doc/equations/special_functions_blurb17.svg index 88e5dbfb3..bb959cb36 100644 --- a/doc/equations/special_functions_blurb17.svg +++ b/doc/equations/special_functions_blurb17.svg @@ -1,2 +1,2 @@ - + asinh(x)=log(x+x2+1) \ No newline at end of file diff --git a/doc/equations/special_functions_blurb18.svg b/doc/equations/special_functions_blurb18.svg index c8df28f5b..7a3be4ea3 100644 --- a/doc/equations/special_functions_blurb18.svg +++ b/doc/equations/special_functions_blurb18.svg @@ -1,2 +1,2 @@ - 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+ sinh(x)=exp(x)−exp(−x)2 \ No newline at end of file diff --git a/doc/equations/special_functions_blurb7.svg b/doc/equations/special_functions_blurb7.svg index c4dfd31cd..76b035e6c 100644 --- a/doc/equations/special_functions_blurb7.svg +++ b/doc/equations/special_functions_blurb7.svg @@ -1,2 +1,2 @@ - + tanh(x)=sinh(x)cosh(x) \ No newline at end of file diff --git a/doc/equations/spherical_0.svg b/doc/equations/spherical_0.svg index eb357c794..471f5622c 100644 --- a/doc/equations/spherical_0.svg +++ b/doc/equations/spherical_0.svg @@ -1,2 +1,2 @@ - + Ynm(θ,φ)=2n+14π(n−m)!(n+m)!Pnm(cosθ)eimφ \ No newline at end of file diff --git a/doc/equations/spherical_1.svg b/doc/equations/spherical_1.svg index bd67f5989..0627b8a9c 100644 --- a/doc/equations/spherical_1.svg +++ b/doc/equations/spherical_1.svg @@ -1,2 +1,2 @@ - + Re(Ynm(θ,φ))=2n+14π(n−m)!(n+m)!Pnm(cosθ)cos(mφ) \ No newline at end of file diff --git a/doc/equations/spherical_2.svg b/doc/equations/spherical_2.svg index 0266a7d5b..2fbbe1ba9 100644 --- a/doc/equations/spherical_2.svg +++ b/doc/equations/spherical_2.svg @@ -1,2 +1,2 @@ - 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+ ζ(s)=∑k=1∞1ks \ No newline at end of file diff --git a/doc/equations/zeta2.svg b/doc/equations/zeta2.svg index ffcdb60bb..bf5fc046c 100644 --- a/doc/equations/zeta2.svg +++ b/doc/equations/zeta2.svg @@ -1,2 +1,2 @@ - + ζ(s)=11−21−s∑n=0∞12n+1∑k=0n(−1)k(nk)(k+1)−s \ No newline at end of file diff --git a/doc/equations/zeta3.svg b/doc/equations/zeta3.svg index bac64d66d..e7e71543b 100644 --- a/doc/equations/zeta3.svg +++ b/doc/equations/zeta3.svg @@ -1,2 +1,2 @@ - + ζ(1−s)=2sin(π1−s2)(2π−s)Γ(s)ζ(s) \ No newline at end of file diff --git a/doc/equations/zeta4.svg b/doc/equations/zeta4.svg index 76829bcb5..2b6ce6eca 100644 --- a/doc/equations/zeta4.svg +++ b/doc/equations/zeta4.svg @@ -1,2 +1,2 @@ - + ς(s)=C+R(1−s)−s1−s \ No newline at end of file diff --git a/doc/equations/zeta5.svg b/doc/equations/zeta5.svg index d34e59534..8dd13f008 100644 --- a/doc/equations/zeta5.svg +++ b/doc/equations/zeta5.svg @@ -1,2 +1,2 @@ - + ς(s)=C+R(s−n)+1s−1 \ No newline at end of file diff --git a/doc/equations/zeta6.svg b/doc/equations/zeta6.svg index 0ec0db7dd..03dc8c806 100644 --- a/doc/equations/zeta6.svg +++ b/doc/equations/zeta6.svg @@ -1,2 +1,2 @@ - + ζ(s)=−1sn(1−21−s)∑j=02n−1ej(j+1)s+γ(s);ej=(−1)j(∑k=0j−nn!k!(n−k)!−2n)∧|γn(s)|<=18n|1−21−s| \ No newline at end of file diff --git a/doc/graphs/acosh.svg b/doc/graphs/acosh.svg index 3b70317c0..d186aea3e 100644 --- a/doc/graphs/acosh.svg +++ b/doc/graphs/acosh.svg @@ -1,64 +1,64 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 - -0.5 -1 -1.5 -2 -2.5 -3 - -acosh(z) - -z - - - - -acosh - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 + +0.5 +1 +1.5 +2 +2.5 +3 + +acosh(z) + +z + + + + +acosh + + + diff --git a/doc/graphs/airy_ai.svg b/doc/graphs/airy_ai.svg index b8e8e2bf6..e618cba03 100644 --- a/doc/graphs/airy_ai.svg +++ b/doc/graphs/airy_ai.svg @@ -1,65 +1,65 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -0 -10 -20 -0 --10 --20 - -0 -0.1 -0.2 -0.3 -0.4 -0.5 -0 --0.1 --0.2 --0.3 --0.4 - -airy_ai(z) - -z - - - - -Ai - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +0 +10 +20 +0 +-10 +-20 + +0 +0.1 +0.2 +0.3 +0.4 +0.5 +0 +-0.1 +-0.2 +-0.3 +-0.4 + +airy_ai(z) + +z + + + + +Ai + + + diff --git a/doc/graphs/airy_aip.svg b/doc/graphs/airy_aip.svg index cef75dc24..711358c89 100644 --- a/doc/graphs/airy_aip.svg +++ b/doc/graphs/airy_aip.svg @@ -1,60 +1,60 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -0 -10 -20 -0 --10 --20 - -0 -0.5 -1 -0 --0.5 --1 - -airy_ai_prime(z) - -z - - - - -Ai' - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +0 +10 +20 +0 +-10 +-20 + +0 +0.5 +1 +0 +-0.5 +-1 + +airy_ai_prime(z) + +z + + + + +Ai' + + + diff --git a/doc/graphs/airy_bi.svg b/doc/graphs/airy_bi.svg index 079840f9c..73f07d4e5 100644 --- a/doc/graphs/airy_bi.svg +++ b/doc/graphs/airy_bi.svg @@ -1,58 +1,58 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -0 -0 --5 --10 --15 --20 - -0 -5 -10 -0 - -airy_bi(z) - -z - - - - -Bi - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +0 +0 +-5 +-10 +-15 +-20 + +0 +5 +10 +0 + +airy_bi(z) + +z + + + + +Bi + + + diff --git a/doc/graphs/airy_bip.svg b/doc/graphs/airy_bip.svg index eca86ee13..cea96e617 100644 --- a/doc/graphs/airy_bip.svg +++ b/doc/graphs/airy_bip.svg @@ -1,60 +1,60 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -0 -0 --5 --10 --15 --20 - 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- - - - - - - - - - - - - - - - - - - - - -0 -1 -0 - -0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1 -1.1 -0 - -Probability - -Random Variable - - - - - - - - - - - -p=0.25 -p=0.5 -p=0.75 - -Bernoulli Distribution CDF - - - + + + + + + + + + + + + + + + + + + + + + + +0 +1 +0 + +0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +1 +1.1 +0 + +Probability + +Random Variable + + + + + + + + + + + +p=0.25 +p=0.5 +p=0.75 + +Bernoulli Distribution CDF + + + diff --git a/doc/graphs/bernoulli_pdf.svg b/doc/graphs/bernoulli_pdf.svg index 4e68853c0..d6f1d3f5e 100644 --- a/doc/graphs/bernoulli_pdf.svg +++ b/doc/graphs/bernoulli_pdf.svg @@ -1,65 +1,65 @@ - - - - - - - - - - - - - - - - - - - - - - -0 -1 -0 - -0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0 - -Probability - -Random Variable - - - - - - - - - - - -p=0.25 -p=0.5 -p=0.75 - -Bernoulli Distribution PDF - - - + + + + + + + + + + + + + + + + + + + + + + +0 +1 +0 + +0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0 + +Probability + +Random Variable + + + + + + + + + + + +p=0.25 +p=0.5 +p=0.75 + +Bernoulli Distribution PDF + + + diff --git a/doc/graphs/beta.svg b/doc/graphs/beta.svg index 3d073e319..bc48101bf 100644 --- a/doc/graphs/beta.svg +++ b/doc/graphs/beta.svg @@ -1,73 +1,73 @@ - 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- - - - - - - - - - - - - - - - - - - - - - - - - - - - -0.5 -1 -1.5 -2 -2.5 -3 - -0 -5 -10 -0 --5 - -jacobi_cs(k, u) - -k - - - - - - - - - - - - - - - -k=0 -k=0.5 -k=0.75 -k=0.95 -k=1 - -Jacobi Elliptic cs - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +0.5 +1 +1.5 +2 +2.5 +3 + +0 +5 +10 +0 +-5 + +jacobi_cs(k, u) + +k + + + + + + + + + + + + + + + +k=0 +k=0.5 +k=0.75 +k=0.95 +k=1 + +Jacobi Elliptic cs + + + diff --git a/doc/graphs/jacobi_dc.svg b/doc/graphs/jacobi_dc.svg index 0668ab03f..3a45fc48c 100644 --- a/doc/graphs/jacobi_dc.svg +++ b/doc/graphs/jacobi_dc.svg @@ -1,76 +1,76 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -0 -5 -10 -0 --5 --10 - -0 -50 -0 --50 --100 - -jacobi_dc(k, u) - -k - - - - - - - - - - - - - - - -k=0 -k=0.5 -k=0.75 -k=0.95 -k=1 - -Jacobi Elliptic dc - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +0 +5 +10 +0 +-5 +-10 + +0 +50 +0 +-50 +-100 + +jacobi_dc(k, u) + +k + + + + + + + + + + + + + + + +k=0 +k=0.5 +k=0.75 +k=0.95 +k=1 + +Jacobi Elliptic dc + + + diff --git a/doc/graphs/jacobi_dn.svg b/doc/graphs/jacobi_dn.svg index 2715c2de2..5e141e733 100644 --- a/doc/graphs/jacobi_dn.svg +++ b/doc/graphs/jacobi_dn.svg @@ -1,81 +1,81 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -0 -5 -10 -0 --5 --10 - -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1 - -jacobi_dn(k, u) - -k - - - - - - - - - - - - - - - -k=0 -k=0.5 -k=0.75 -k=0.95 -k=1 - -Jacobi Elliptic dn - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +0 +5 +10 +0 +-5 +-10 + +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +1 + +jacobi_dn(k, u) + +k + + + + + + + + + + + + + + + +k=0 +k=0.5 +k=0.75 +k=0.95 +k=1 + +Jacobi Elliptic dn + + + diff --git a/doc/graphs/jacobi_ds.svg b/doc/graphs/jacobi_ds.svg index 4db06920c..97bac8b91 100644 --- a/doc/graphs/jacobi_ds.svg +++ b/doc/graphs/jacobi_ds.svg @@ -1,81 +1,81 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -0.5 -1 -1.5 -2 -2.5 -3 - -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 - -jacobi_ds(k, u) - -k - - - - - - - - - - - - - - - -k=0 -k=0.5 -k=0.75 -k=0.95 -k=1 - -Jacobi Elliptic ds - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +0.5 +1 +1.5 +2 +2.5 +3 + +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 + +jacobi_ds(k, u) + +k + + + + + + + + + + + + + + + +k=0 +k=0.5 +k=0.75 +k=0.95 +k=1 + +Jacobi Elliptic ds + + + diff --git a/doc/graphs/jacobi_nc.svg b/doc/graphs/jacobi_nc.svg index 1f850bf4c..ab1dbdaa4 100644 --- a/doc/graphs/jacobi_nc.svg +++ b/doc/graphs/jacobi_nc.svg @@ -1,83 +1,83 @@ - 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- - - - - - - - - - - - - - - - - - - - - - - - - - - - -1 -2 -3 -4 - -0 -0 --500 --1e3 --1.5e3 --2e3 - -jacobi_ns(k, u) - -k - - - - - - - - - - - - - - - -k=0 -k=0.5 -k=0.75 -k=0.95 -k=1 - -Jacobi Elliptic ns - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +1 +2 +3 +4 + +0 +0 +-500 +-1e3 +-1.5e3 +-2e3 + +jacobi_ns(k, u) + +k + + + + + + + + + + + + + + + +k=0 +k=0.5 +k=0.75 +k=0.95 +k=1 + +Jacobi Elliptic ns + + + diff --git a/doc/graphs/jacobi_sc.svg b/doc/graphs/jacobi_sc.svg index 7f7ab88ae..8d2b72f59 100644 --- a/doc/graphs/jacobi_sc.svg +++ b/doc/graphs/jacobi_sc.svg @@ -1,85 +1,85 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -0 -1 -2 -3 -4 -5 -0 --1 --2 --3 --4 --5 - -0 -100 -200 -300 -0 --100 --200 --300 - -jacobi_sc(k, u) - -k - - - - - - - - - - - - - - - -k=0 -k=0.5 -k=0.75 -k=0.95 -k=1 - -Jacobi Elliptic sc - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +0 +1 +2 +3 +4 +5 +0 +-1 +-2 +-3 +-4 +-5 + +0 +100 +200 +300 +0 +-100 +-200 +-300 + +jacobi_sc(k, u) + +k + + + + + + + + + + + + + + + +k=0 +k=0.5 +k=0.75 +k=0.95 +k=1 + +Jacobi Elliptic sc + + + diff --git a/doc/graphs/jacobi_sd.svg b/doc/graphs/jacobi_sd.svg index 2a147cbb9..311ba7011 100644 --- a/doc/graphs/jacobi_sd.svg +++ b/doc/graphs/jacobi_sd.svg @@ -1,75 +1,75 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -0 -1 -2 -0 --1 --2 - -0 -5 -0 --5 - -jacobi_sd(k, u) - -k - - - - - - - - - - - - - - - -k=0 -k=0.5 -k=0.75 -k=0.95 -k=1 - -Jacobi Elliptic sd - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +0 +1 +2 +0 +-1 +-2 + +0 +5 +0 +-5 + +jacobi_sd(k, u) + +k + + + + + + + + + + + + + + + +k=0 +k=0.5 +k=0.75 +k=0.95 +k=1 + +Jacobi Elliptic sd + + + diff --git a/doc/graphs/jacobi_sn.svg b/doc/graphs/jacobi_sn.svg index 383f5c285..8174a6c7b 100644 --- a/doc/graphs/jacobi_sn.svg +++ b/doc/graphs/jacobi_sn.svg @@ -1,76 +1,76 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -0 -5 -10 -0 --5 --10 - -0 -0.5 -1 -0 --0.5 - -jacobi_sn(k, u) - -k - - - - - - - - - - - - - - - -k=0 -k=0.5 -k=0.75 -k=0.95 -k=1 - -Jacobi Elliptic sn - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +0 +5 +10 +0 +-5 +-10 + +0 +0.5 +1 +0 +-0.5 + +jacobi_sn(k, u) + +k + + + + + + + + + + + + + + + +k=0 +k=0.5 +k=0.75 +k=0.95 +k=1 + +Jacobi Elliptic sn + + + diff --git a/doc/graphs/laguerre.svg b/doc/graphs/laguerre.svg index 47d47c7cd..a3a3e97e1 100644 --- a/doc/graphs/laguerre.svg +++ b/doc/graphs/laguerre.svg @@ -1,78 +1,78 @@ - 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