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The substitution <math>x \rightarrow \arccos(x)</math> transforms Matheiu's equation to the ''rational form''
:<math> y^{\prime \prime} = \frac{x}{1-x^2} \, y^\prime + \frac{( 4x^2-2) \, q -a}{1-x^2} \, y</math>
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
=Floquet solution==
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