7.19.2 Factorials
Although factorials can be computed from the Gamma function, using
the relation n! = \Gamma(n+1) for non-negative integer n,
it is usually more efficient to call the functions in this section,
particularly for small values of n, whose factorial values are
maintained in hardcoded tables.
— Function: double
gsl_sf_fact (
unsigned int n)
— Function: int
gsl_sf_fact_e (
unsigned int n, gsl_sf_result * result)
These routines compute the factorial n!. The factorial is
related to the Gamma function by n! = \Gamma(n+1).
The maximum value of n such that n! is not
considered an overflow is given by the macro GSL_SF_FACT_NMAX
and is 170.
— Function: double
gsl_sf_doublefact (
unsigned int n)
— Function: int
gsl_sf_doublefact_e (
unsigned int n, gsl_sf_result * result)
These routines compute the double factorial n!! = n(n-2)(n-4) \dots.
The maximum value of n such that n!! is not
considered an overflow is given by the macro GSL_SF_DOUBLEFACT_NMAX
and is 297.
— Function: double
gsl_sf_lnfact (
unsigned int n)
— Function: int
gsl_sf_lnfact_e (
unsigned int n, gsl_sf_result * result)
These routines compute the logarithm of the factorial of n,
\log(n!). The algorithm is faster than computing
\ln(\Gamma(n+1)) via gsl_sf_lngamma for n < 170,
but defers for larger n.
— Function: double
gsl_sf_lndoublefact (
unsigned int n)
— Function: int
gsl_sf_lndoublefact_e (
unsigned int n, gsl_sf_result * result)
These routines compute the logarithm of the double factorial of n,
\log(n!!).
— Function: double
gsl_sf_choose (
unsigned int n, unsigned int m)
— Function: int
gsl_sf_choose_e (
unsigned int n, unsigned int m, gsl_sf_result * result)
These routines compute the combinatorial factor n choose m
= n!/(m!(n-m)!)
— Function: double
gsl_sf_lnchoose (
unsigned int n, unsigned int m)
— Function: int
gsl_sf_lnchoose_e (
unsigned int n, unsigned int m, gsl_sf_result * result)
These routines compute the logarithm of n choose m. This is
equivalent to the sum \log(n!) - \log(m!) - \log((n-m)!).
— Function: double
gsl_sf_taylorcoeff (
int n, double x)
— Function: int
gsl_sf_taylorcoeff_e (
int n, double x, gsl_sf_result * result)
These routines compute the Taylor coefficient x^n / n! for
x >= 0,
n >= 0.