= Mathieu characteristic value
{c}
{title2=$a_n(q),\ b_n(q)$}
The Mathieu characteristic values are the parameter values $a$ for which the <Mathieu equation> has the even periodic mode traditionally denoted $\operatorname{ce}_n$, or the odd periodic mode $\operatorname{se}_n$. They are <eigenvalues> of $-d^2/dt^2+2q\cos2t$ with the corresponding periodic or antiperiodic <boundary conditions>. Their small-$q$ expansions can be derived by projecting onto a <Fourier series> and perturbing the resulting tridiagonal <matrix>.
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