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Gegenbauer polynomials: Graphs and documentation. [CI SKIP]

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NAThompson
2019-08-04 15:59:12 -04:00
parent a733b75005
commit 9efeb19046
5 changed files with 198 additions and 1 deletions
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doc/sf/gegenbauer.qbk
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@@ -43,7 +43,7 @@ The /k/-th derivative of the /n/-th Gegenbauer polynomial is given by
unsigned k = 2;
double y = gegenbauer_derivative(n, lambda, x, k);
[$../graphs/gegenbauer.svg]
[h3 Implementation]
@@ -97,5 +97,10 @@ The relative accuracy cannot be controlled at the roots of the polynomial, as is
[$../graphs/gegenbauer_ulp_5.svg]
[$../graphs/gegenbauer_ulp_9.svg]
[h3 Caveats]
Some programs define the Gegenbauer polynomial with \u03BB = 0 via renormalization (which makes them Chebyshev polynomials).
We do not follow this convention: In this case, only the zeroth Gegenbauer polynomial is nonzero.
[endsect]