Solution of Inhomogeneous Differential Equations with Polynomial Coefficients in Nonstandard Analysis, in Terms of the Green's Function

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 a preceding paper, solution is given without using the Green's function, on the basis of nonstandard analysis, for a restricted class of inhomogeneous terms. In the present paper, the corresponding solutions are given in terms of the Green's function. It is applied to Kummer's and the hypergeometric differential equation.