Generalized-hypergeometric solutions of the general Fuchsian linear ODE having five regular singularities

TL;DR

This paper demonstrates that a Fuchsian differential equation with five regular singular points can be solved using a generalized hypergeometric function for infinitely many parameter choices, under specific restrictions.

Contribution

It introduces a method to express solutions of such Fuchsian equations in terms of generalized hypergeometric functions with particular parameter restrictions.

Findings

Solutions exist for infinitely many parameter sets.

Restrictions include integer exponents at two singularities.

Accessory parameters satisfy polynomial equations.

Abstract

We show that a Fuchsian differential equation having five regular singular points admits solutions in terms of a single generalized hypergeometric function for infinitely many particular choices of equation parameters. Each solution assumes four restrictions imposed on the parameters: two of the singularities should have non-zero integer characteristic exponents and the accessory parameters should obey polynomial equations.