High-Order Coefficients of Second-Order ODEs in Relation to Pre-Factors for Complex Parameter

Abstract

In this study, we asymptotically reconsider the relations between the pre-factors of a general inhomogeneous second-order ordinary differential equation and the high-order coefficients of its asymptotic power series for complex values of the asymptotic parameter $ \epsilon_{1} $. The study provides a general formula for its generic high-order coefficients with the associated pre-factors for complex $ \epsilon_{1} $ based on the use of a well-known factorial divided by a power approach.