summaryrefslogtreecommitdiff
path: root/gsl-1.9/doc/specfunc-laguerre.texi
diff options
context:
space:
mode:
Diffstat (limited to 'gsl-1.9/doc/specfunc-laguerre.texi')
-rw-r--r--gsl-1.9/doc/specfunc-laguerre.texi40
1 files changed, 40 insertions, 0 deletions
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