Mathieu function: Difference between revisions

Revision as of 23:36, 3 October 2005

Revision as of 23:38, 3 October 2005

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These are closely related to the Floquet solution:

:<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>

For small values of q, these functions do resemble sine and cosine near the origin. In the example plotted below (same values of a,q as above), the Mathieu cosine is plotted in red and cosine in green:

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

[[Image:MathieuCosine.gif|center]]

==Periodic solutions==