Mathieu function: Difference between revisions

Revision as of 23:05, 29 May 2005

Revision as of 11:50, 3 October 2005

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:<math> \frac{d^2y}{dx^2}+[p-2q\cos (2x) ]y=0 </math>

The Mathieu equation and its solutions are theused basisin to understand the phenomenon oftreating [[parametric resonance]]. The equation and function are named after [[Emile Mathieu]].

The Mathieu functions are analogous to sine and cosine, but have different periods.

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== External links Definition==

The '''Mathieu cosine''' <math>MC(a,b,\xi)</math> is the unique solution of the Mathieu equation which is

#an [[even function]],

#takes the value <math>MC(a,b,0)=1</math>.

Similarly, the '''Mathieu sine''' <math>MS(a,b,\xi)</math> is the unique solution which is

#an [[odd function]],

#takes the value

== Symbolic computation engines ==

Various special functions related to the Mathieu functions are implemented in [[Maple]] and [[Mathematica]].

==External links==

*[http://mathworld.wolfram.com/MathieuFunction.html Mathworld] at Wolfram

*[http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Mathieu_Emile.html Emile Mathieu biography] at [[St. Andrews University]]

*[http://eqworld.ipmnet.ru/en/ EqWorld] offers a useful page on the Mathieu equation.

==References==

*{{Template:Book reference | Author=McLachlan, N. W. | Title=Theory and application of Mathieu functions | Publisher=New York: Dover | Year=1962 (reprint of 1947 ed.) | ID=LCCN 64016333}}

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[[Category:Special functions]]