# On a new identity for the H-function with applications to the summation of hypergeometric series

## TL;DR

This paper introduces a new identity for the H-function, enabling the splitting of complex functions into simpler parts, which aids in summing hypergeometric series and connecting H-functions with elementary functions.

## Contribution

A novel identity for the H-function is derived, allowing it to be expressed as a sum of two H-functions, enhancing symbolic manipulation capabilities.

## Key findings

- New identity enables splitting H-functions into sums.
- Application to summation of hypergeometric series.
- Relations established between H-functions and elementary functions.

## Abstract

Using generalized hypergeometric functions to perform symbolic manipulation of equations is of great importance to pure and applied scientists. There are in the literature a great number of identities for the Meijer-G function. On the other hand, when more complex expressions arise, the latter function is not capable of representing them. The H-function is an alternative to overcome this issue, as it is a generalization of the Meijer-G function. In the present paper, a new identity for the H-function is derived. In short, this result enables one to split a particular H-function into the sum of two other H-functions. The new relation in addition to an old result are applied to the summation of hypergeometric series. Finally, some relations between H-functions and elementary functions are built