| @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 |
