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@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
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