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

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 s...

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Bibliographic Details
Published in:Applied mathematics and computation 2003-07, Vol.139 (1), p.165-178
Main Authors: KIYMAZ, Onur, MIRASYEDIOGLU, Seref
Format: Article
Language:English
Subjects:
Exact sciences and technology
Generalized hypergeometric series
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Power series solutions
Sciences and techniques of general use
Special functions
Symbolic computation
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Summary: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.
ISSN:0096-3003
1873-5649
DOI:10.1016/S0096-3003(02)00208-4