Solution of Inhomogeneous Differential Equations with Polynomial Coefficients in Nonstandard Analysis, in Terms of the Green's Function
Tohru Morita *
Graduate School of Information Sciences, Tohoku University, Sendai 980-8577, Japan.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Green's function, differential equations with polynomial coefficients, nonstandard analysis, Kummer's differential equation, hypergeometric differential equation