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 generalinhomogeneous second-order ordinary differential equation and the high-order coefficientsof its asymptotic power series for complex values of the asymptotic parameter $varepsilon_1$. Thestudy provides a general formula for its generic high-order coefficients with the associatedpre-factors for complex $varepsilon_1$ based on the use of a well-known factorial divided by a powerapproach.