A symbolic algorithm for exact power series solutions of nth order linear homogeneous differential equations with polynomial coefficients near an ordinary point

摘要

We developed an algorithm in Kıymaz and Mirasyedioğlu [O. Kıymaz and Ş. Mirasyedioğlu, An algorithmic approach to exact power series solutions of second order linear homogeneous differential equations with polynomial coefficients, Appl. Math. Comp. 139 (1) (2003) 165–178] for computing exact power series solutions of second order linear homogeneous differential equations with polynomial coefficients, near a point x = x0. In this paper we present a symbolic algorithm to compute the exact power series solutions of nth order linear homogeneous differential equations with polynomial coefficients, near an ordinary point.