Mathieu function: Difference between revisions

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\frac{d^2y}{dx^2} + (a - 2q\cos 2x)y = 0,

</math>

where <math>a</math> and <math>q</math> are parameters. They were first introduced by [[Émile Léonard Mathieu]], who encountered them while studying vibrating elliptical drumheads.<ref>Mathieu (1868).</ref><ref name="MorseandFeshbach">Morse and Feshbach (1953).</ref> They have applications in many fields of the physical sciences, such as [[optics]], [[quantum mechanics]], and [[general relativity]]. They tend to occur in problems involving periodic motion, or in the analysis of [[partial differential equation]] [[boundary value problem]]s possessing [[elliptic]]{{Disambiguation needed|date=August 2020}} symmetry.<ref name="Gutiérrez-Vega2015">Gutiérrez-Vega (2015).</ref>

== Definition ==