Mathieu function: Difference between revisions

Revision as of 23:32, 3 October 2005

Revision as of 23:34, 3 October 2005

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==Mathieu sine and cosine==

[[Image:MatheiuCosine.gif|frame|right|Mathieu cosine C(1,0.2,x), in red, and cos(x) for comparison, in green.]]

For fixed a,q, the '''Mathieu cosine''' <math>C(a,q,\xi)</math> is a function of <math>\xi</math> defined as the unique solution of the Mathieu equation which

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:<math> C(a,q,x) = \frac{\exp(i \mu)}{F(a,q,0} \, \frac{P(a,q,x) + P(a,q,-x)}{2}</math>

:<math> S(a,q,x) = \frac{\exp(i \mu)}{F(a,q,0} \, \frac{P(a,q,x) - P(a,q,-x)}{2}</math>

[[Image:MatheiuCosineMathieuCosine.gif|frame|rightcenter|Mathieu cosine C(1,0.2,x), in red, and cos(x) for comparison, in green.]]

==Periodic solutions==