`scipy.special._basic:mathieu_odd_coef`

source: /scipy/special/_basic.py :1642

Signature

def mathieu_odd_coef ( m , q )

Summary

Fourier coefficients for odd Mathieu and modified Mathieu functions.

Extended Summary

The Fourier series of the odd solutions of the Mathieu differential equation are of the form

se_{2 n + 1} (z, q) = k = 0 \sum \infty B_{(2 n + 1)}^{(2 k + 1)} sin (2 k + 1) z

se_{2 n + 2} (z, q) = k = 0 \sum \infty B_{(2 n + 2)}^{(2 k + 2)} sin (2 k + 2) z

This function returns the coefficients $B_{(2 n + 2)}^{(2 k + 2)}$ for even input m=2n+2, and the coefficients $B_{(2 n + 1)}^{(2 k + 1)}$ for odd input m=2n+1.

Parameters

m : int: Order of Mathieu functions. Must be non-negative.
q : float (>=0): Parameter of Mathieu functions. Must be non-negative.

Returns

Bk : ndarray: Even or odd Fourier coefficients, corresponding to even or odd m.

Aliases

scipy.special.mathieu_odd_coef