An Application of the Infinite Matrix Theory to Mathieu Equation

In this paper we study the infinite linear system MμX = 0 equivalent to the Mathieu equation. Applying some results in summability we determine the Floquet exponents corresponding to the solutions of the differential equation. We also determine an approximation of the corresponding solutions and study the kernel of the operator represented by Mμ. Finally we deal with the Mathieu equation with a second member.