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This has two regular singularities at x = -1,1 and one irregularity singularity at infinity, whic impleis that in general (unlike many other special functions), the solutions of Mathieu's equation ''cannot'' be expressed in terms of [[hypergeometric function]]s.
==Floquet solution==
According to [[Floquet's theorem]], for fixed values of a,q, Mathieu's equation admits a ''complex valued'' solution of form
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