— Function: int gsl_sf_mathieu_a (int n, double q, gsl_sf_result * result)
— Function: int gsl_sf_mathieu_b (int n, double q, gsl_sf_result * result)

These routines compute the characteristic values a_n(q), b_n(q) of the Mathieu functions ce_n(q,x) and se_n(q,x), respectively.

— Function: int gsl_sf_mathieu_a_array (int order_min, int order_max, double q, gsl_sf_mathieu_workspace * work, double result_array[])
— Function: int gsl_sf_mathieu_b_array (int order_min, int order_max, double q, gsl_sf_mathieu_workspace * work, double result_array[])

These routines compute a series of Mathieu characteristic values a_n(q), b_n(q) for n from order_min to order_max inclusive, storing the results in the array result_array.