Mathieu function: Difference between revisions

Revision as of 00:24, 4 October 2005

Revision as of 00:25, 4 October 2005

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==Periodic solutions==

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 Mathieu cosine, sine functions respectively are written <math>a_n(q), \, b_n(q)</math>, where n in '''N'''. The periodic special cases of the Mathieu cosine and sine functions are often written <math>CE(n,q,x), \, SE(n,q,x)</math> respectively. Here are the first few periodic Mathieu cosine functions:

Here are the first few periodic Mathieu cosine functions:

[[Image:MathieuCE.gif|center]]

Here,Note <math>CE(1that,0,x)</math> (red) is sinusoidal, but none of the others are. Forfor example, <math>CE(1,1,x)</math> (green) is obviously too flat near the origin to be a sinusoidal function.

== Symbolic computation engines ==