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

Authors:
Onur Kiymaz;Şeref Mirasyedioğlu
Affiliations:
Department of Mathematics Education, Gazi University, Egitim Fakultesi, K-Blok, 06500 Teknikokullar-Ankara, Turkey;Department of Mathematics Education, Gazi University, Egitim Fakultesi, K-Blok, 06500 Teknikokullar-Ankara, Turkey
Venue:
Applied Mathematics and Computation
Year:
2003

Citing 5
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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 = x0, if its recurrence equation is hypergeometric type. The algorithm, which has been implemented in MAPLE, is based on symbolic computation.