Connection problem for the generalized hypergeometric function

TL;DR

This paper addresses the connection problem for the generalized hypergeometric function by deriving explicit connection coefficients between solutions at singular points 0 and 1, using analytic continuation of integral representations.

Contribution

It provides explicit formulas for connection coefficients as products of sine and cosecant functions, advancing understanding of hypergeometric functions' analytic structure.

Findings

Derived explicit connection coefficients between singular points 0 and 1

Expressed connection coefficients as products of sine and cosecant functions

Enhanced the analytic continuation framework for hypergeometric functions

Abstract

We solve connection problem between fundamental solutions at singular points $0$ and $1$ for the generalized hypergeometric function, using analytic continuation of the integral representation. All connection coefficients are products of the sine and the cosecant.