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Diffstat (limited to 'gsl-1.9/doc/specfunc-gegenbauer.texi')
| -rw-r--r-- | gsl-1.9/doc/specfunc-gegenbauer.texi | 42 |
1 files changed, 42 insertions, 0 deletions
diff --git a/gsl-1.9/doc/specfunc-gegenbauer.texi b/gsl-1.9/doc/specfunc-gegenbauer.texi new file mode 100644 index 0000000..949c3dd --- /dev/null +++ b/gsl-1.9/doc/specfunc-gegenbauer.texi @@ -0,0 +1,42 @@ +@cindex Gegenbauer functions + +The Gegenbauer polynomials are defined in Abramowitz & Stegun, Chapter +22, where they are known as Ultraspherical polynomials. The functions +described in this section are declared in the header file +@file{gsl_sf_gegenbauer.h}. + +@deftypefun double gsl_sf_gegenpoly_1 (double @var{lambda}, double @var{x}) +@deftypefunx double gsl_sf_gegenpoly_2 (double @var{lambda}, double @var{x}) +@deftypefunx double gsl_sf_gegenpoly_3 (double @var{lambda}, double @var{x}) +@deftypefunx int gsl_sf_gegenpoly_1_e (double @var{lambda}, double @var{x}, gsl_sf_result * @var{result}) +@deftypefunx int gsl_sf_gegenpoly_2_e (double @var{lambda}, double @var{x}, gsl_sf_result * @var{result}) +@deftypefunx int gsl_sf_gegenpoly_3_e (double @var{lambda}, double @var{x}, gsl_sf_result * @var{result}) +These functions evaluate the Gegenbauer polynomials +@c{$C^{(\lambda)}_n(x)$} +@math{C^@{(\lambda)@}_n(x)} using explicit +representations for @math{n =1, 2, 3}. +@comment Exceptional Return Values: none +@end deftypefun + + +@deftypefun double gsl_sf_gegenpoly_n (int @var{n}, double @var{lambda}, double @var{x}) +@deftypefunx int gsl_sf_gegenpoly_n_e (int @var{n}, double @var{lambda}, double @var{x}, gsl_sf_result * @var{result}) +These functions evaluate the Gegenbauer polynomial @c{$C^{(\lambda)}_n(x)$} +@math{C^@{(\lambda)@}_n(x)} for a specific value of @var{n}, +@var{lambda}, @var{x} subject to @math{\lambda > -1/2}, @c{$n \ge 0$} +@math{n >= 0}. +@comment Domain: lambda > -1/2, n >= 0 +@comment Exceptional Return Values: GSL_EDOM +@end deftypefun + + +@deftypefun int gsl_sf_gegenpoly_array (int @var{nmax}, double @var{lambda}, double @var{x}, double @var{result_array}[]) +This function computes an array of Gegenbauer polynomials +@c{$C^{(\lambda)}_n(x)$} +@math{C^@{(\lambda)@}_n(x)} for @math{n = 0, 1, 2, \dots, nmax}, subject +to @math{\lambda > -1/2}, @c{$nmax \ge 0$} +@math{nmax >= 0}. +@comment Conditions: n = 0, 1, 2, ... nmax +@comment Domain: lambda > -1/2, nmax >= 0 +@comment Exceptional Return Values: GSL_EDOM +@end deftypefun |