specfunc-laguerre.texi

This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY without ev

@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