# Some summation theorems for truncated Clausen series and applications

## TL;DR

This paper derives new summation theorems for truncated Clausen hypergeometric series with specific parameter conditions and applies these results to obtain Mellin transforms involving Goursat's truncated hypergeometric function.

## Contribution

It introduces novel summation theorems for truncated Clausen series with negative integer parameters and applies them to Mellin transforms of related functions.

## Key findings

- New summation theorems for truncated Clausen series
- Explicit Mellin transforms involving Goursat's hypergeometric function
- Enhanced understanding of hypergeometric series with negative parameters

## Abstract

The main aim of this paper is to derive some new summation theorems for terminating and truncated Clausen's hypergeometric series with unit argument, when one numerator parameter and one denominator parameter are negative integers. Further, using our truncated summation theorems, we obtain the Mellin transforms of the product of exponential function and Goursat's truncated hypergeometric function.