A note on values of $ {}_{4}F_{3} $ hypergeometric functions

TL;DR

This paper extends Gauss's summation identity to compute specific values of $_4F_3$ hypergeometric functions, generalizing previous results and providing new formulas for these special functions.

Contribution

It introduces an extended Gauss's summation identity and applies it to evaluate a family of $_4F_3$ hypergeometric functions, broadening existing knowledge.

Findings

Derived an extended Gauss's summation identity.

Computed explicit values for a family of $_4F_3$ hypergeometric functions.

Generalized previous results by Ferretti et al.

Abstract

In this note, we firstly establish an extended Gauss's summation identity. Using this identity, we compute values of a family of $_4F_3$ hypergeometric functions, which generalize the results obtained by Ferretti et al..