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

Kiymaz O., Mirasyedioglu S.

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


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.