— Function: double gsl_sf_beta (double a, double b)
— Function: int gsl_sf_beta_e (double a, double b, gsl_sf_result * result)

These routines compute the Beta Function, B(a,b) = \Gamma(a)\Gamma(b)/\Gamma(a+b) subject to a and b not being negative integers.

— Function: double gsl_sf_lnbeta (double a, double b)
— Function: int gsl_sf_lnbeta_e (double a, double b, gsl_sf_result * result)

These routines compute the logarithm of the Beta Function, \log(B(a,b)) subject to a and b not being negative integers.