A summation formula for a ${}_3F_2(1)$ hypergeometric series

TL;DR

This paper derives a new summation formula for a specific class of hypergeometric series, expanding the mathematical tools available for analyzing these special functions.

Contribution

The paper introduces a novel summation formula for the ${}_3F_2(1)$ hypergeometric series with parameters involving an integer index, under certain real part conditions.

Findings

Provides a closed-form summation formula for the series

Extends existing hypergeometric identities

Offers potential applications in mathematical analysis

Abstract

A summation formula is derived for the hypergeometric series of unit argument ${}_3F_2(1,1,c;d,n+2;1)$, where $n=0, 1, 2, \ldots$ and $\Re (d-c+n)>0$.