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SciPy

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scipy.special.mathieu_odd_coef

scipy.special.mathieu_odd_coef(m, q)[source]

Fourier coefficients for even Mathieu and modified Mathieu functions.

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

se2n+1(z,q)=k=0B(2k+1)(2n+1)sin(2k+1)z
se2n+2(z,q)=k=0B(2k+2)(2n+2)sin(2k+2)z

This function returns the coefficients B(2k+2)(2n+2) for even input m=2n+2, and the coefficients B(2k+1)(2n+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.

References

[R431]Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. http://jin.ece.illinois.edu/specfunc.html