GNU Scientific Library – Reference Manual: Radial Mathieu Functions

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#### 7.26.4 Radial Mathieu Functions

Function: int gsl_sf_mathieu_Mc (int j, int n, double q, double x)
Function: int gsl_sf_mathieu_Mc_e (int j, int n, double q, double x, gsl_sf_result * result)
Function: int gsl_sf_mathieu_Ms (int j, int n, double q, double x)
Function: int gsl_sf_mathieu_Ms_e (int j, int n, double q, double x, gsl_sf_result * result)

  These routines compute the radial j-th kind Mathieu functions Mc_n^{(j)}(q,x) and Ms_n^{(j)}(q,x) of order n.

  The allowed values of j are 1 and 2. The functions for j = 3,4 can be computed as M_n^{(3)} = M_n^{(1)} + iM_n^{(2)} and M_n^{(4)} = M_n^{(1)} - iM_n^{(2)}, where M_n^{(j)} = Mc_n^{(j)} or Ms_n^{(j)}.

Function: int gsl_sf_mathieu_Mc_array (int j, int nmin, int nmax, double q, double x, gsl_sf_mathieu_workspace * work, double result_array[])
Function: int gsl_sf_mathieu_Ms_array (int j, int nmin, int nmax, double q, double x, gsl_sf_mathieu_workspace * work, double result_array[])

  These routines compute a series of the radial Mathieu functions of kind j, with order from nmin to nmax inclusive, storing the results in the array result_array.