Zeta Functions
==============

Riemann Zeta Function
---------------------

The Riemann zeta function is defined by

 -- Function: int gsl_sf_zeta_int_impl (int n, gsl_sf_result * result)
 -- Function: int gsl_sf_zeta_int_e (int n, gsl_sf_result * result)
     Domain: n integer, n != 1 Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW

 -- Function: int gsl_sf_zeta_impl (double s, gsl_sf_result * result)
 -- Function: int gsl_sf_zeta_e (double s, gsl_sf_result * result)
     Domain: s != 1.0 Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW

Hurwitz Zeta Function
---------------------

The Hurwitz zeta function is defined by zeta(s,q) = \sum_0^\infty (k+q)^(-s) .

 -- Function: int gsl_sf_hzeta_impl (double s, double q, gsl_sf_result * result)
 -- Function: int gsl_sf_hzeta_e (double s, double q, gsl_sf_result * result)
     Domain: s > 1.0, q > 0.0 Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW, GSL_EOVRFLW

Eta Function
------------

The eta function is defined by \eta(s) = (1-2^(1-s)) zeta(s) .

 -- Function: int gsl_sf_eta_int_impl (int n, gsl_sf_result * result)
 -- Function: int gsl_sf_eta_int_e (int n, gsl_sf_result * result)
     Exceptional Return Values: GSL_EUNDRFLW, GSL_EOVRFLW

 -- Function: int gsl_sf_eta_impl (double s, gsl_sf_result * result)
 -- Function: int gsl_sf_eta_e (double s, gsl_sf_result * result)
     Exceptional Return Values: GSL_EUNDRFLW, GSL_EOVRFLW