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scipy.special.mathieu_even_coef¶
- scipy.special.mathieu_even_coef(m, q)[source]¶
Fourier coefficients for even Mathieu and modified Mathieu functions.
The Fourier series of the even solutions of the Mathieu differential equation are of the form
ce2n(z,q)=∞∑k=0A(2k)(2n)cos2kzce2n+1(z,q)=∞∑k=0A(2k+1)(2n+1)cos(2k+1)zThis function returns the coefficients A(2k)(2n) for even input m=2n, and the coefficients A(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: Ak : ndarray
Even or odd Fourier coefficients, corresponding to even or odd m.
References
[R429] Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. http://jin.ece.illinois.edu/specfunc.html [R430] NIST Digital Library of Mathematical Functions http://dlmf.nist.gov/28.4#i