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, cilt.139, sa.1, ss.165-178, 2003 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 139 Konu: 1
  • Basım Tarihi: 2003
  • Doi Numarası: 10.1016/s0096-3003(02)00208-4
  • Sayfa Sayıları: ss.165-178


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.