GNU Scientific Library – Reference Manual: Mathieu Function Characteristic Values

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#### 7.26.2 Mathieu Function Characteristic Values

Function: int gsl_sf_mathieu_a (int n, double q)
Function: int gsl_sf_mathieu_a_e (int n, double q, gsl_sf_result * result)
Function: int gsl_sf_mathieu_b (int n, double q)
Function: int gsl_sf_mathieu_b_e (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.