mirror of
https://github.com/boostorg/math.git
synced 2026-01-19 16:32:10 +00:00
Added mml and svg versions of most of the equations.
[SVN r39541]
This commit is contained in:
John Maddock
49
doc/equations/beta1.mml
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49
doc/equations/beta1.mml
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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<mrow>
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<mtext>beta</mtext>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>,</mo>
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<mi>b</mi>
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</mrow>
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</mfenced>
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<mo>=</mo>
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<mi>B</mi>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>,</mo>
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<mi>b</mi>
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</mrow>
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</mfenced>
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<mo>=</mo>
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<mfrac>
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<mrow>
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<mi>Γ</mi>
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<mfenced>
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<mrow>
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<mi>a</mi>
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</mrow>
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</mfenced>
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<mi>Γ</mi>
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<mfenced>
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<mrow>
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<mi>b</mi>
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</mrow>
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</mfenced>
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</mrow>
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<mrow>
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<mi>Γ</mi>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>+</mo>
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<mi>b</mi>
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</mrow>
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</mfenced>
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</mrow>
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</mfrac>
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</mrow>
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</math>
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2
doc/equations/beta1.svg
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2
doc/equations/beta1.svg
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After Width: | Height: | Size: 6.6 KiB |
106
doc/equations/beta2.mml
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106
doc/equations/beta2.mml
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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<mrow>
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<mtext>beta</mtext>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>,</mo>
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<mi>b</mi>
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</mrow>
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</mfenced>
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<mo>=</mo>
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<msup>
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<mfenced>
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<mrow>
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<mfrac>
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<mrow>
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<mi>a</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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<mrow>
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<mi>a</mi>
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<mo>+</mo>
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<mi>b</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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</mfrac>
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</mrow>
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</mfenced>
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<mrow>
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<mi>a</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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</msup>
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<msup>
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<mfenced>
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<mrow>
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<mfrac>
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<mrow>
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<mi>b</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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<mrow>
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<mi>a</mi>
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<mo>+</mo>
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<mi>b</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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</mfrac>
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</mrow>
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</mfenced>
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<mi>b</mi>
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</msup>
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<msqrt>
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<mrow>
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<mfrac>
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<mi>e</mi>
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<mrow>
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<mi>b</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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</mfrac>
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</mrow>
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</msqrt>
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<mfrac>
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<mrow>
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<mi>L</mi>
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<mfenced>
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<mrow>
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<mi>a</mi>
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</mrow>
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</mfenced>
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<mi>L</mi>
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<mfenced>
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<mrow>
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<mi>b</mi>
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</mrow>
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</mfenced>
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</mrow>
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<mrow>
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<mi>L</mi>
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<mfenced>
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<mrow>
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<mi>c</mi>
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</mrow>
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</mfenced>
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</mrow>
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</mfrac>
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</mrow>
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</math>
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2
doc/equations/beta2.svg
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2
doc/equations/beta2.svg
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After Width: | Height: | Size: 13 KiB |
128
doc/equations/beta3.mml
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128
doc/equations/beta3.mml
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@@ -0,0 +1,128 @@
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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<mrow>
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<mtext>beta</mtext>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>,</mo>
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<mi>b</mi>
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</mrow>
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</mfenced>
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<mo>=</mo>
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<msup>
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<mfenced>
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<mrow>
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<mfrac>
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<mrow>
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<mi>a</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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<mrow>
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<mi>a</mi>
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<mo>+</mo>
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<mi>b</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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</mfrac>
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</mrow>
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</mfenced>
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<mrow>
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<mi>a</mi>
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<mo>−</mo>
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<mi>b</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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</msup>
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<msup>
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<mfenced>
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<mrow>
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<mfrac>
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<mrow>
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<mfenced>
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||||
<mrow>
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<mi>a</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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</mfenced>
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<mfenced>
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<mrow>
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<mi>b</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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</mfenced>
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</mrow>
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<mrow>
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<msup>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>+</mo>
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<mi>b</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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</mfenced>
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<mn>2</mn>
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</msup>
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</mrow>
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</mfrac>
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</mrow>
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</mfenced>
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<mi>b</mi>
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</msup>
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<msqrt>
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<mrow>
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<mfrac>
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<mi>e</mi>
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<mrow>
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<mi>b</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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</mfrac>
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</mrow>
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</msqrt>
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<mfrac>
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<mrow>
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<mi>L</mi>
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<mfenced>
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<mrow>
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<mi>a</mi>
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</mrow>
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</mfenced>
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<mi>L</mi>
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<mfenced>
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<mrow>
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<mi>b</mi>
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</mrow>
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</mfenced>
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</mrow>
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<mrow>
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<mi>L</mi>
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<mfenced>
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<mrow>
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<mi>c</mi>
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</mrow>
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</mfenced>
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</mrow>
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</mfrac>
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</mrow>
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</math>
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2
doc/equations/beta3.svg
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2
doc/equations/beta3.svg
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After Width: | Height: | Size: 16 KiB |
34
doc/equations/beta4.mml
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34
doc/equations/beta4.mml
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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<mrow>
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<mtext>beta</mtext>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>,</mo>
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<mi>b</mi>
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</mrow>
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</mfenced>
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<mo>=</mo>
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<mfrac>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>+</mo>
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<mi>b</mi>
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</mrow>
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</mfenced>
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<mi>b</mi>
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</mfrac>
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<mtext>beta</mtext>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>,</mo>
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<mi>b</mi>
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<mo>+</mo>
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<mn>1</mn>
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</mrow>
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</mfenced>
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</mrow>
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</math>
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2
doc/equations/beta4.svg
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2
doc/equations/beta4.svg
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After Width: | Height: | Size: 5.0 KiB |
49
doc/equations/beta5.mml
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49
doc/equations/beta5.mml
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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<mrow>
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<mtext>beta</mtext>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>,</mo>
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<mi>b</mi>
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</mrow>
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</mfenced>
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<mo>=</mo>
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<mfrac>
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<mrow>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>+</mo>
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<mi>b</mi>
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</mrow>
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</mfenced>
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<mfenced>
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||||
<mrow>
|
||||
<mi>a</mi>
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<mo>+</mo>
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<mi>b</mi>
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||||
<mo>+</mo>
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<mn>1</mn>
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</mrow>
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||||
</mfenced>
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</mrow>
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<mrow>
|
||||
<mi>a</mi>
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<mi>b</mi>
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</mrow>
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</mfrac>
|
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<mtext>beta</mtext>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>+</mo>
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<mn>1,</mn>
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<mi>b</mi>
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||||
<mo>+</mo>
|
||||
<mn>1</mn>
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||||
</mrow>
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</mfenced>
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</mrow>
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</math>
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2
doc/equations/beta5.svg
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2
doc/equations/beta5.svg
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After Width: | Height: | Size: 6.9 KiB |
48
doc/equations/beta6.mml
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48
doc/equations/beta6.mml
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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<mrow>
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<mi>i</mi>
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||||
<mi>f</mi>
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||||
<mspace width="1em"/>
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<mi>a</mi>
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<mo>≫</mo>
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<mi>b</mi>
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||||
<mspace width="1em"/>
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||||
<mi>a</mi>
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||||
<mi>n</mi>
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||||
<mi>d</mi>
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||||
<mspace width="1em"/>
|
||||
<mi>a</mi>
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||||
<mo>+</mo>
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||||
<mi>b</mi>
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||||
<mo>=</mo>
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||||
<mi>a</mi>
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||||
<mspace width="1em"/>
|
||||
<mspace width="1em"/>
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||||
<mi>t</mi>
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||||
<mi>h</mi>
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||||
<mi>e</mi>
|
||||
<mi>n</mi>
|
||||
<mo>:</mo>
|
||||
<mspace width="1em"/>
|
||||
<mspace width="1em"/>
|
||||
<mi>b</mi>
|
||||
<mi>e</mi>
|
||||
<mi>t</mi>
|
||||
<mi>a</mi>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>a</mi>
|
||||
<mo>,</mo>
|
||||
<mi>b</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mo>=</mo>
|
||||
<mi>Γ</mi>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>b</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mrow>
|
||||
</math>
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||||
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||||
2
doc/equations/beta6.svg
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2
doc/equations/beta6.svg
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After Width: | Height: | Size: 7.4 KiB |
28
doc/equations/beta7.mml
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doc/equations/beta7.mml
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||||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
||||
<mrow>
|
||||
<mtext>if</mtext>
|
||||
<mspace width="1em"/>
|
||||
<mi>a</mi>
|
||||
<mo>=</mo>
|
||||
<mn>1</mn>
|
||||
<mspace width="1em"/>
|
||||
<mspace width="1em"/>
|
||||
<mtext>then:</mtext>
|
||||
<mspace width="1em"/>
|
||||
<mspace width="1em"/>
|
||||
<mtext>beta</mtext>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>a</mi>
|
||||
<mo>,</mo>
|
||||
<mi>b</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mo>=</mo>
|
||||
<mfrac>
|
||||
<mn>1</mn>
|
||||
<mi>b</mi>
|
||||
</mfrac>
|
||||
</mrow>
|
||||
</math>
|
||||
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||||
2
doc/equations/beta7.svg
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doc/equations/beta7.svg
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||||
<?xml version="1.0" encoding="utf-8"?>
|
||||
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doc/equations/chi_squ_tut2.svg
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doc/equations/chi_squ_tut3.mml
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doc/equations/chi_squ_tut3.svg
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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53
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Normal file
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Normal file
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Normal file
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Normal file
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Normal file
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Normal file
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Normal file
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doc/equations/ellint20.svg
Normal file
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|
||||
<mi>R</mi>
|
||||
<mi>F</mi>
|
||||
</msub>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<msup>
|
||||
<mi>cos</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mn>1</mn>
|
||||
<mo>−</mo>
|
||||
<msup>
|
||||
<mi>k</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<msup>
|
||||
<mi>sin</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mn>1</mn>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mo>−</mo>
|
||||
<mrow>
|
||||
<mfrac>
|
||||
<mn>1</mn>
|
||||
<mn>3</mn>
|
||||
</mfrac>
|
||||
</mrow>
|
||||
<msup>
|
||||
<mi>k</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mi>sin</mi>
|
||||
<msup>
|
||||
<mi/>
|
||||
<mn>3</mn>
|
||||
</msup>
|
||||
<mi>φ</mi>
|
||||
<msub>
|
||||
<mi>R</mi>
|
||||
<mi>D</mi>
|
||||
</msub>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>cos</mi>
|
||||
<msup>
|
||||
<mi/>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mn>1</mn>
|
||||
<mo>−</mo>
|
||||
<msup>
|
||||
<mi>k</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mi>sin</mi>
|
||||
<msup>
|
||||
<mi/>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mn>1</mn>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mtd>
|
||||
</mtr>
|
||||
</mtable>
|
||||
</mrow>
|
||||
</math>
|
||||
|
||||
2
doc/equations/ellint21.svg
Normal file
2
doc/equations/ellint21.svg
Normal file
File diff suppressed because one or more lines are too long
|
After Width: | Height: | Size: 22 KiB |
57
doc/equations/ellint22.mml
Normal file
57
doc/equations/ellint22.mml
Normal file
@@ -0,0 +1,57 @@
|
||||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
||||
<mrow>
|
||||
<mi>E</mi>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>k</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mspace width="1em"/>
|
||||
<mo>=</mo>
|
||||
<mspace width="1em"/>
|
||||
<msub>
|
||||
<mi>R</mi>
|
||||
<mi>F</mi>
|
||||
</msub>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mn>0,1</mn>
|
||||
<mo>−</mo>
|
||||
<msup>
|
||||
<mi>k</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mo>,</mo>
|
||||
<mn>1</mn>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mo>−</mo>
|
||||
<mrow>
|
||||
<mfrac>
|
||||
<mn>1</mn>
|
||||
<mn>3</mn>
|
||||
</mfrac>
|
||||
</mrow>
|
||||
<msup>
|
||||
<mi>k</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<msub>
|
||||
<mi>R</mi>
|
||||
<mi>D</mi>
|
||||
</msub>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mn>0,1</mn>
|
||||
<mo>−</mo>
|
||||
<msup>
|
||||
<mi>k</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mo>,</mo>
|
||||
<mn>1</mn>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mrow>
|
||||
</math>
|
||||
|
||||
2
doc/equations/ellint22.svg
Normal file
2
doc/equations/ellint22.svg
Normal file
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|
After Width: | Height: | Size: 6.8 KiB |
130
doc/equations/ellint23.mml
Normal file
130
doc/equations/ellint23.mml
Normal file
@@ -0,0 +1,130 @@
|
||||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
||||
<mrow>
|
||||
<mtable>
|
||||
<mtr>
|
||||
<mtd>
|
||||
<mo>∏</mo>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>n</mi>
|
||||
<mo>,</mo>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mn>0</mn>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<mo>=</mo>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<msqrt>
|
||||
<mrow>
|
||||
<mfrac>
|
||||
<mn>1</mn>
|
||||
<mrow>
|
||||
<mn>1</mn>
|
||||
<mo>−</mo>
|
||||
<mi>n</mi>
|
||||
</mrow>
|
||||
</mfrac>
|
||||
</mrow>
|
||||
</msqrt>
|
||||
<msup>
|
||||
<mi>tan</mi>
|
||||
<mrow>
|
||||
<mo>−</mo>
|
||||
<mn>1</mn>
|
||||
</mrow>
|
||||
</msup>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<msqrt>
|
||||
<mrow>
|
||||
<mn>1</mn>
|
||||
<mo>−</mo>
|
||||
<mi>n</mi>
|
||||
</mrow>
|
||||
</msqrt>
|
||||
<mi>tan</mi>
|
||||
<mi>φ</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<mo>;</mo>
|
||||
<mi>n</mi>
|
||||
<mo><</mo>
|
||||
<mn>1</mn>
|
||||
</mtd>
|
||||
</mtr>
|
||||
<mtr>
|
||||
<mtd>
|
||||
<mspace width="1em"/>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<mo>=</mo>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<msqrt>
|
||||
<mrow>
|
||||
<mfrac>
|
||||
<mn>1</mn>
|
||||
<mrow>
|
||||
<mi>n</mi>
|
||||
<mo>−</mo>
|
||||
<mn>1</mn>
|
||||
</mrow>
|
||||
</mfrac>
|
||||
</mrow>
|
||||
</msqrt>
|
||||
<msup>
|
||||
<mi>tanh</mi>
|
||||
<mrow>
|
||||
<mo>−</mo>
|
||||
<mn>1</mn>
|
||||
</mrow>
|
||||
</msup>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<msqrt>
|
||||
<mrow>
|
||||
<mi>n</mi>
|
||||
<mo>−</mo>
|
||||
<mn>1</mn>
|
||||
</mrow>
|
||||
</msqrt>
|
||||
<mi>tan</mi>
|
||||
<mi>φ</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<mo>;</mo>
|
||||
<mi>n</mi>
|
||||
<mo>></mo>
|
||||
<mn>1</mn>
|
||||
</mtd>
|
||||
</mtr>
|
||||
<mtr>
|
||||
<mtd>
|
||||
<mspace width="1em"/>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<mo>=</mo>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<mi>tan</mi>
|
||||
<mi>φ</mi>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<mo>;</mo>
|
||||
<mi>n</mi>
|
||||
<mo>=</mo>
|
||||
<mn>1</mn>
|
||||
</mtd>
|
||||
</mtr>
|
||||
</mtable>
|
||||
</mrow>
|
||||
</math>
|
||||
|
||||
2
doc/equations/ellint23.svg
Normal file
2
doc/equations/ellint23.svg
Normal file
File diff suppressed because one or more lines are too long
|
After Width: | Height: | Size: 14 KiB |
224
doc/equations/ellint24.mml
Normal file
224
doc/equations/ellint24.mml
Normal file
@@ -0,0 +1,224 @@
|
||||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
||||
<mrow>
|
||||
<mtable>
|
||||
<mtr>
|
||||
<mtd>
|
||||
<msqrt>
|
||||
<mrow>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mn>1</mn>
|
||||
<mo>−</mo>
|
||||
<mi>n</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mn>1</mn>
|
||||
<mo>−</mo>
|
||||
<mfrac>
|
||||
<msup>
|
||||
<mi>k</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mi>n</mi>
|
||||
</mfrac>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mrow>
|
||||
</msqrt>
|
||||
<mo>∏</mo>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>n</mi>
|
||||
<mo>,</mo>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mi>k</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<mo>=</mo>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<msqrt>
|
||||
<mrow>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mn>1</mn>
|
||||
<mo>−</mo>
|
||||
<mi>N</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mn>1</mn>
|
||||
<mo>−</mo>
|
||||
<mfrac>
|
||||
<msup>
|
||||
<mi>k</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mi>N</mi>
|
||||
</mfrac>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mrow>
|
||||
</msqrt>
|
||||
<mo>∏</mo>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>N</mi>
|
||||
<mo>,</mo>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mi>k</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mtd>
|
||||
</mtr>
|
||||
<mtr>
|
||||
<mtd>
|
||||
<mspace width="1em"/>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<mo>+</mo>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<mfrac>
|
||||
<msup>
|
||||
<mi>k</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mrow>
|
||||
<msub>
|
||||
<mi>p</mi>
|
||||
<mn>2</mn>
|
||||
</msub>
|
||||
</mrow>
|
||||
</mfrac>
|
||||
<mi>F</mi>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mi>k</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mtd>
|
||||
</mtr>
|
||||
<mtr>
|
||||
<mtd>
|
||||
<mspace width="1em"/>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<mo>+</mo>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<msup>
|
||||
<mi>tan</mi>
|
||||
<mrow>
|
||||
<mo>−</mo>
|
||||
<mn>1</mn>
|
||||
</mrow>
|
||||
</msup>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mfrac>
|
||||
<msub>
|
||||
<mi>p</mi>
|
||||
<mn>2</mn>
|
||||
</msub>
|
||||
<mn>2</mn>
|
||||
</mfrac>
|
||||
<mfrac>
|
||||
<mrow>
|
||||
<mi>sin</mi>
|
||||
<mrow>
|
||||
<mn>2</mn>
|
||||
<mi>φ</mi>
|
||||
</mrow>
|
||||
</mrow>
|
||||
<mrow>
|
||||
<mtext>?</mtext>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>φ</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mrow>
|
||||
</mfrac>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mtd>
|
||||
</mtr>
|
||||
<mtr>
|
||||
<mtd>
|
||||
<mi>N</mi>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<mo>=</mo>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<mfrac>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<msup>
|
||||
<mi>k</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mo>−</mo>
|
||||
<mi>n</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mn>1</mn>
|
||||
<mo>−</mo>
|
||||
<mi>n</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mfrac>
|
||||
</mtd>
|
||||
</mtr>
|
||||
<mtr>
|
||||
<mtd>
|
||||
<msub>
|
||||
<mi>p</mi>
|
||||
<mn>2</mn>
|
||||
</msub>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<mo>=</mo>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<msqrt>
|
||||
<mrow>
|
||||
<mo>−</mo>
|
||||
<mfrac>
|
||||
<mi>n</mi>
|
||||
<mrow>
|
||||
<mn>1</mn>
|
||||
<mo>−</mo>
|
||||
<mi>n</mi>
|
||||
</mrow>
|
||||
</mfrac>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<msup>
|
||||
<mi>k</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mo>−</mo>
|
||||
<mi>n</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mrow>
|
||||
</msqrt>
|
||||
</mtd>
|
||||
</mtr>
|
||||
</mtable>
|
||||
</mrow>
|
||||
</math>
|
||||
|
||||
2
doc/equations/ellint24.svg
Normal file
2
doc/equations/ellint24.svg
Normal file
File diff suppressed because one or more lines are too long
|
After Width: | Height: | Size: 23 KiB |
93
doc/equations/ellint25.mml
Normal file
93
doc/equations/ellint25.mml
Normal file
@@ -0,0 +1,93 @@
|
||||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
||||
<mrow>
|
||||
<mo>∏</mo>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>n</mi>
|
||||
<mo>,</mo>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mi>k</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mspace width="1em"/>
|
||||
<mo>=</mo>
|
||||
<mspace width="1em"/>
|
||||
<mi>sin</mi>
|
||||
<mi>φ</mi>
|
||||
<msub>
|
||||
<mi>R</mi>
|
||||
<mi>F</mi>
|
||||
</msub>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>cos</mi>
|
||||
<msup>
|
||||
<mi/>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mn>1</mn>
|
||||
<mo>−</mo>
|
||||
<msup>
|
||||
<mi>k</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mi>sin</mi>
|
||||
<msup>
|
||||
<mi/>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mn>1</mn>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mo>+</mo>
|
||||
<mfrac>
|
||||
<mi>n</mi>
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||||
</mfenced>
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||||
<mspace width="1em"/>
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<mo>=</mo>
|
||||
<mspace width="1em"/>
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<mfrac>
|
||||
<mi>z</mi>
|
||||
<mrow>
|
||||
<mn>1</mn>
|
||||
<mo>−</mo>
|
||||
<mfrac>
|
||||
<msup>
|
||||
<mi>z</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mrow>
|
||||
<mn>3</mn>
|
||||
<mo>−</mo>
|
||||
<mfrac>
|
||||
<msup>
|
||||
<mi>z</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mrow>
|
||||
<mn>5</mn>
|
||||
<mo>−</mo>
|
||||
<mfrac>
|
||||
<msup>
|
||||
<mi>z</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mrow>
|
||||
<mn>7</mn>
|
||||
<mo>−</mo>
|
||||
<mfrac>
|
||||
<msup>
|
||||
<mi>z</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mrow>
|
||||
<mn>9</mn>
|
||||
<mo>−</mo>
|
||||
<mo>…</mo>
|
||||
</mrow>
|
||||
</mfrac>
|
||||
</mrow>
|
||||
</mfrac>
|
||||
</mrow>
|
||||
</mfrac>
|
||||
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|
||||
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|
||||
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|
||||
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|
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||||
</math>
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2
doc/equations/fraction4.svg
Normal file
2
doc/equations/fraction4.svg
Normal file
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|
After Width: | Height: | Size: 6.5 KiB |
43
doc/equations/gamm1.mml
Normal file
43
doc/equations/gamm1.mml
Normal file
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|
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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||||
<mrow>
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||||
<mtext>tgamma</mtext>
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<mfenced>
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||||
<mrow>
|
||||
<mi>z</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mo>=</mo>
|
||||
<mi>Γ</mi>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>z</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mo>=</mo>
|
||||
<munderover>
|
||||
<mo>∫</mo>
|
||||
<mrow>
|
||||
<mn>0</mn>
|
||||
</mrow>
|
||||
<mi>∞</mi>
|
||||
</munderover>
|
||||
<msup>
|
||||
<mi>t</mi>
|
||||
<mrow>
|
||||
<mi>z</mi>
|
||||
<mo>−</mo>
|
||||
<mn>1</mn>
|
||||
</mrow>
|
||||
</msup>
|
||||
<msup>
|
||||
<mi>e</mi>
|
||||
<mrow>
|
||||
<mo>−</mo>
|
||||
<mi>t</mi>
|
||||
</mrow>
|
||||
</msup>
|
||||
<mi>d</mi>
|
||||
<mi>t</mi>
|
||||
</mrow>
|
||||
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|
||||
|
||||
2
doc/equations/gamm1.svg
Normal file
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doc/equations/gamm1.svg
Normal file
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|
After Width: | Height: | Size: 5.0 KiB |
130
doc/equations/gamm2.mml
Normal file
130
doc/equations/gamm2.mml
Normal file
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|
||||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
||||
<mrow>
|
||||
<mi>Γ</mi>
|
||||
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|
||||
<mrow>
|
||||
<mi>z</mi>
|
||||
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|
||||
</mfenced>
|
||||
<mo>=</mo>
|
||||
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|
||||
<mrow>
|
||||
<msup>
|
||||
<mi>l</mi>
|
||||
<mi>a</mi>
|
||||
</msup>
|
||||
<msup>
|
||||
<mi>e</mi>
|
||||
<mrow>
|
||||
<mo>−</mo>
|
||||
<mi>l</mi>
|
||||
</mrow>
|
||||
</msup>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<munderover>
|
||||
<mo>∑</mo>
|
||||
<mrow>
|
||||
<mn>0</mn>
|
||||
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|
||||
<mi>∞</mi>
|
||||
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|
||||
<mrow>
|
||||
<mfrac>
|
||||
<msup>
|
||||
<mi>l</mi>
|
||||
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|
||||
</msup>
|
||||
<msup>
|
||||
<mi>a</mi>
|
||||
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|
||||
<mover>
|
||||
<mi>n</mi>
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
<mo>+</mo>
|
||||
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|
||||
<mn>1</mn>
|
||||
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|
||||
<mi>a</mi>
|
||||
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|
||||
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|
||||
<msub>
|
||||
<mi>c</mi>
|
||||
<mn>1</mn>
|
||||
</msub>
|
||||
<mrow>
|
||||
<msub>
|
||||
<mi>d</mi>
|
||||
<mn>1</mn>
|
||||
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|
||||
<mo>+</mo>
|
||||
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|
||||
<msub>
|
||||
<mi>c</mi>
|
||||
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|
||||
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|
||||
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|
||||
<msub>
|
||||
<mi>d</mi>
|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
<msub>
|
||||
<mi>d</mi>
|
||||
<mn>3</mn>
|
||||
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|
||||
<mo>+</mo>
|
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|
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|
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<mo>;</mo>
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<msub>
|
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<mi>c</mi>
|
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|
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|
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<mo>=</mo>
|
||||
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|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>a</mi>
|
||||
<mo>+</mo>
|
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|
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|
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|
||||
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|
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|
||||
<mo>∧</mo>
|
||||
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|
||||
<mi>d</mi>
|
||||
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|
||||
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|
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<mo>=</mo>
|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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2
doc/equations/gamm2.svg
Normal file
2
doc/equations/gamm2.svg
Normal file
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|
After Width: | Height: | Size: 14 KiB |
25
doc/equations/gamm3.mml
Normal file
25
doc/equations/gamm3.mml
Normal file
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|
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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<mrow>
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<mi>Γ</mi>
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|
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|
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|
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|
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|
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2
doc/equations/gamm3.svg
Normal file
2
doc/equations/gamm3.svg
Normal file
@@ -0,0 +1,2 @@
|
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<?xml version="1.0" encoding="utf-8"?>
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|
After Width: | Height: | Size: 3.1 KiB |
28
doc/equations/gamm4.mml
Normal file
28
doc/equations/gamm4.mml
Normal file
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|
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|
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|
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<mi>Γ</mi>
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|
||||
|
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2
doc/equations/gamm4.svg
Normal file
2
doc/equations/gamm4.svg
Normal file
@@ -0,0 +1,2 @@
|
||||
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<svg:svg xmlns="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" height="20.857500pt" width="67.009797pt" xmlns:svgmath="http://www.grigoriev.ru/svgmath" viewBox="0 -13.693359 67.009797 20.857500"><svg:metadata><svgmath:metrics top="20.8575" bottom="0.0" baseline="7.164140625" axis="11.148515625"/></svg:metadata><svg:g transform="translate(0.186211, 0.000000)"><svg:text font-size="12.000000" text-anchor="middle" y="0.000000" x="8.000977" font-family="Times New Roman" fill="black">lim</svg:text></svg:g><svg:g transform="translate(0.000000, 7.064297)"><svg:text font-size="8.520000" text-anchor="middle" y="0.000000" x="1.911592" font-family="Times New Roman" font-style="italic" fill="black">z</svg:text><svg:g transform="translate(3.594375, -2.828906)"><svg:text font-size="8.520000" text-anchor="middle" y="2.828906" x="4.260000" font-family="Times New Roman" fill="black">→</svg:text></svg:g><svg:g transform="translate(12.114375, 0.000000)"><svg:text font-size="8.520000" text-anchor="middle" y="0.000000" x="2.130000" font-family="Times New Roman" fill="black">0</svg:text></svg:g></svg:g><svg:g transform="translate(16.374375, 0.000000)"><svg:g transform="translate(0.000000, -3.984375)"><svg:text font-size="12.012889" transform="scale(0.998927, 1)" text-anchor="middle" y="3.981593" x="2.000193" font-family="Times New Roman" fill="black">(</svg:text></svg:g><svg:g transform="translate(3.996094, 0.000000)"><svg:text font-size="12.000000" text-anchor="middle" y="0.000000" x="3.846680" font-family="Times New Roman" font-style="italic" fill="black">Γ</svg:text><svg:g transform="translate(8.396484, 0.000000)"><svg:g transform="translate(0.000000, -3.984375)"><svg:text font-size="12.012889" transform="scale(0.998927, 1)" text-anchor="middle" y="3.981593" x="2.000193" font-family="Times New Roman" fill="black">(</svg:text></svg:g><svg:g transform="translate(3.996094, 0.000000)"><svg:text font-size="12.000000" text-anchor="middle" y="0.000000" x="2.692383" font-family="Times New Roman" font-style="italic" fill="black">z</svg:text></svg:g><svg:g transform="translate(9.058594, -3.984375)"><svg:text font-size="12.012889" transform="scale(0.998927, 1)" text-anchor="middle" y="3.981593" x="2.000193" font-family="Times New Roman" fill="black">)</svg:text></svg:g></svg:g></svg:g><svg:g transform="translate(25.447266, -3.984375)"><svg:text font-size="12.012889" transform="scale(0.998927, 1)" text-anchor="middle" y="3.981593" x="2.000193" font-family="Times New Roman" fill="black">)</svg:text></svg:g></svg:g><svg:g transform="translate(49.151070, -3.984375)"><svg:text font-size="12.000000" text-anchor="middle" y="3.984375" x="3.383789" font-family="Times New Roman" fill="black">=</svg:text></svg:g><svg:g transform="translate(59.837922, -3.984375)"><svg:g transform="translate(0.585938, -1.599609)"><svg:text font-size="12.000000" text-anchor="middle" y="0.000000" x="3.000000" font-family="Times New Roman" fill="black">1</svg:text></svg:g><svg:g transform="translate(1.054688, 6.761719)"><svg:text font-size="12.000000" text-anchor="middle" y="0.000000" x="2.692383" font-family="Times New Roman" font-style="italic" fill="black">z</svg:text></svg:g><svg:line y2="0.000000" stroke-width="0.585938" x2="7.171875" stroke="black" stroke-linecap="butt" stroke-dasharray="none" y1="0.000000" x1="0.000000" fill="none"/></svg:g></svg:svg>
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||||
|
After Width: | Height: | Size: 3.3 KiB |
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user