Finding all bessel type solutions for linear differential equations with rational function coefficients

Authors:
Mark van Hoeij;Quan Yuan
Affiliations:
Florida State University, Tallahassee, FL;Florida State University, Tallahassee, FL
Venue:
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Year:
2010

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Abstract

A linear differential equation with rational function coefficients has a Bessel type solution when it is solvable in terms of Bv(f), Bv+1(f). For second order equations, with rational function coefficients, f must be a rational function or the square root of a rational function. An algorithm was given by Debeerst, van Hoeij, and Koepf, that can compute Bessel type solutions if and only if f is a rational function. In this paper we extend this work to the square root case, resulting in a complete algorithm to find all Bessel type solutions.