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

摘要

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.