Solution of Inhomogeneous and Homogeneous Heun’s Differential Equations in Nonstandard Analysis

Discussions are presented by Morita and Sato on the problem of obtaining the particular solution of an inhomogeneous differential equation with polynomial coefficients in terms of the Green’s function. In succeeding papers, Morita gave discussions of this problem on the basis of nonstandard analysis. It was applied to the hypergeometric, the Hermite, a simple ordinary and a fractional differential equation. In the present paper, this method is applied to the solutions of inhomogeneous and homogeneous Heun’s differential equations.