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Diffstat (limited to 'gsl-1.9/doc/specfunc-laguerre.texi')
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diff --git a/gsl-1.9/doc/specfunc-laguerre.texi b/gsl-1.9/doc/specfunc-laguerre.texi new file mode 100644 index 0000000..8672d59 --- /dev/null +++ b/gsl-1.9/doc/specfunc-laguerre.texi @@ -0,0 +1,40 @@ +@cindex Laguerre functions +@cindex confluent hypergeometric function + +The generalized Laguerre polynomials are defined in terms of confluent +hypergeometric functions as +@c{$L^a_n(x) = ((a+1)_n / n!) {}_1F_1(-n,a+1,x)$} +@math{L^a_n(x) = ((a+1)_n / n!) 1F1(-n,a+1,x)}, and are sometimes referred to as the +associated Laguerre polynomials. They are related to the plain +Laguerre polynomials @math{L_n(x)} by @math{L^0_n(x) = L_n(x)} and +@c{$L^k_n(x) = (-1)^k (d^k/dx^k) L_{(n+k)}(x)$} +@math{L^k_n(x) = (-1)^k (d^k/dx^k) L_(n+k)(x)}. For +more information see Abramowitz & Stegun, Chapter 22. + +The functions described in this section are +declared in the header file @file{gsl_sf_laguerre.h}. + +@deftypefun double gsl_sf_laguerre_1 (double @var{a}, double @var{x}) +@deftypefunx double gsl_sf_laguerre_2 (double @var{a}, double @var{x}) +@deftypefunx double gsl_sf_laguerre_3 (double @var{a}, double @var{x}) +@deftypefunx int gsl_sf_laguerre_1_e (double @var{a}, double @var{x}, gsl_sf_result * @var{result}) +@deftypefunx int gsl_sf_laguerre_2_e (double @var{a}, double @var{x}, gsl_sf_result * @var{result}) +@deftypefunx int gsl_sf_laguerre_3_e (double @var{a}, double @var{x}, gsl_sf_result * @var{result}) +These routines evaluate the generalized Laguerre polynomials +@math{L^a_1(x)}, @math{L^a_2(x)}, @math{L^a_3(x)} using explicit +representations. +@comment Exceptional Return Values: none +@end deftypefun + + +@deftypefun double gsl_sf_laguerre_n (const int @var{n}, const double @var{a}, const double @var{x}) +@deftypefunx int gsl_sf_laguerre_n_e (int @var{n}, double @var{a}, double @var{x}, gsl_sf_result * @var{result}) +These routines evaluate the generalized Laguerre polynomials +@math{L^a_n(x)} for @math{a > -1}, +@c{$n \ge 0$} +@math{n >= 0}. + +@comment Domain: a > -1.0, n >= 0 +@comment Evaluate generalized Laguerre polynomials. +@comment Exceptional Return Values: GSL_EDOM +@end deftypefun |