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mathieu_even_coef(m, q)

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

$$\mathrm{ce}_{2n}(z, q) = \sum_{k=0}^{\infty} A_{(2n)}^{(2k)} \cos 2kz$$ $$\mathrm{ce}_{2n+1}(z, q) = \sum_{k=0}^{\infty} A_{(2n+1)}^{(2k+1)} \cos (2k+1)z$$

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

Ak : ndarray

Even or odd Fourier coefficients, corresponding to even or odd m.

Fourier coefficients for even Mathieu and modified Mathieu functions.

Examples

See :

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GitHub : /scipy/special/_basic.py#1126
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