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For countably many special values of a, called ''characteristic values'', the Mathieu equation admits solutions which are periodic with period <math>2\pi</math>. The characteristic values of the Mathiue cosine, sine functions respectively are written <math>a_n(q), \, b_n(q)</math>, where n in '''N'''. Here are the first few periodic Mathieu cosine functions:
[[Image:MathieuCE.gif|center]]
Here, <math>CE(1,0,x)</math> (red) is sinusoidal, but none of the others are. For example, <math>CE(1,1,x)</math> (green) is too flat near the origin to be sinusoidal.
== Symbolic computation engines ==
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