Apparent singular points of factors of reducible generalized hypergeometric equations

TL;DR

This paper investigates apparent singular points of reducible generalized hypergeometric equations, identifying the polynomial roots as a generalized hypergeometric polynomial, thus advancing understanding of their singularity structure.

Contribution

It determines the polynomial whose roots are the apparent singular points of reducible generalized hypergeometric equations, showing it is a generalized hypergeometric polynomial.

Findings

Identified the polynomial with roots at apparent singular points

Connected the polynomial to generalized hypergeometric functions

Enhanced understanding of singularity structure in hypergeometric equations

Abstract

We consider a reducible generalized hypergeometric equation, whose sub-equation possesses apparent singular points. We determine the polynomial whose roots are these points. We show that this polynomial is a generalized hypergeometric polynomial. Key Words and Phrases. the generalized hypergeometric equation, reducible, apparent singular point, minor of Wronskian.