# General series identities, some additive theorems on hypergeometric functions and their applications

## TL;DR

This paper develops general series identities involving hypergeometric functions and bounded sequences, and applies these results to various special functions such as trigonometric, elliptic, and gamma functions.

## Contribution

It introduces new rigorous identities for hypergeometric series with broad applicability to many special functions.

## Key findings

- Established general series identities for hypergeometric functions.
- Applied identities to derive results for various special functions.
- Enhanced understanding of relationships among special functions.

## Abstract

Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are generally applicable in nature. For the application purpose, we apply our results to some functions e.g. Trigonometric functions, Elliptic integrals, Dilogarithmic function, Error function, Incomplete gamma function, and many other special functions.