On the construction of solutions of the Mathieu equation by Frobenius-Latysheva method

Abstract

The possibilities of building normal, subnormal and normal - regular solutions of Mathieu algebraic equation by using Frobenius-Latysheva method are studied. The products of Mathieu subnormal series are considered. It is established a second order partial differential equation the solutions of which are the products of Mathieu subnormal series. It is also shown that this subnormal solutions a solution of the initial Mathieu equation with periodic coefficients.