# A new identity for a sum of products of the generalized hypergeometric functions

## TL;DR

This paper introduces a new identity for sums of products of generalized hypergeometric functions, extending previous formulas and connecting various known identities in the field.

## Contribution

It generalizes existing identities by Feng, Kuznetsov, and Yang, encompassing formulas by Ebisu and Gorelov, thus unifying multiple results in hypergeometric function theory.

## Key findings

- Unified a range of identities for hypergeometric functions
- Extended the scope of previous formulas to more general cases
- Provided a new perspective on algebraic properties of hypergeometric functions

## Abstract

Reduction formulas for sums of products of hypergeometric functions can be traced back to Euler. This topic has an intimate connection to summation and transformation formulas, contiguous relations and algebraic properties of the (generalized) hypergeometric differential equation. Over recent several years, important discoveries have been made in this subject by Gorelov, Ebisu, Beukers and Jouhet and Feng, Kuznetsov and Yang. In this paper, we give a generalization of Feng, Kuznetsov and Yang identity covering also Ebisu's and Gorelov's formulas as particular cases.