Abstract
Basically periodic solutions of Mathieu's equation, that is, those with period π or 2π, are commonly called Mathieu functions of the first kind of integral order or simply Mathieu functions. This chapter discusses perturbation method of solution of Mathieu's equation. It illustrates the solution of Mathieu's algebraic equation. Considerable importance, both theoretical and practical, attaches to the problem of expanding a given function in a series of Mathieu functions of integral order, on the lines of Fourier series expansions.
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