An algorithmic approach to exact power series solutions of second order linear homogeneous differential equations with polynomial coefficients

Kiymaz, O; Mirasyedioglu, S

doi:10.1016/s0096-3003(02)00208-4

An algorithmic approach to exact power series solutions of second order linear homogeneous differential equations with polynomial coefficients

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Kiymaz O., Mirasyedioglu S.

APPLIED MATHEMATICS AND COMPUTATION, vol.139, no.1, pp.165-178, 2003 (SCI-Expanded)

Publication Type: Article / Article
Volume: 139 Issue: 1
Publication Date: 2003
Doi Number: 10.1016/s0096-3003(02)00208-4
Journal Name: APPLIED MATHEMATICS AND COMPUTATION
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Page Numbers: pp.165-178
Gazi University Affiliated: No

Abstract

In 1992, Koepf [J. Symb. Comp. 13 (1992) 581] introduced an algorithm for computing a Formal Power Series of a given function using generalized hypergeometric series and a recurrence equation of hypergeometric type. The main aim of this paper is to develop a new algorithm for computing exact power series solutions of second order linear differential equations with polynomial coefficients, near a point x = x(0), if its recurrence equation is hypergeometric type. The algorithm, which has been implemented in MAPLE, is based on symbolic computation. (C) 2002 Elsevier Science Inc. All rights reserved.