# Radial Mathieu functions, divergence problem

I am working on a project that requires the utilization of even Mathieu functions.

This is the definition of my functions:

1. Even Mathieu function: Ce[a, q, z] = MathieuC[a, q, z]
2. Characteristic number of order m: am[q] = MathieuCharacteristicA[m, q]
Cem[q,x] = MathieuC[MathieuCharacteristicA[m, q], q, I x]

In my project, I have to work with the function Cem[q, x] with indexes m = 2 r, r=1, 2, 3, 4, 5, 6, 7, 8, ..., 0 <= q <= 400, and 0 < x < 20.
So, this is the problem: The function Cem[q, x] explodes (becomes very badly behaved) when it is at the range x > 2.5, and get really worse for larger values of q. The next figure shows what I mean. Could anyone give me a suggestion on how to solve this problem? T
• Try raising the WorkingPrecision: Plot[MathieuC[MathieuCharacteristicA[4, 10], 10, I x], {x, 0, 4}, WorkingPrecision -> 100] -- I think this question has been asked before. Jan 12 '20 at 22:30