Some summation theorems for Clausen's hypergeometric functions with unit argument

TL;DR

This paper derives new summation theorems for Clausen's hypergeometric functions at unit argument, expressing results in terms of pi and logarithms, and introduces modified summation formulas.

Contribution

It presents novel summation theorems and modifications for Clausen's hypergeometric functions, expanding the theoretical understanding of these special functions.

Findings

New summation theorems expressed with pi and logarithms

Modified summation formulas for Clausen's hypergeometric functions

Extensions of existing hypergeometric summation results

Abstract

Motivated by the work on hypergeometric summation theorems (recorded in the table III of Prudnikov et al. pp. 541-546), we have established some new summation theorems for Clausen's hypergeometric functions with unit argument in terms of $\pi$ and natural logarithms of some rational and irrational numbers. Also, we have given some modified summation theorems for Clausen's hypergeometric functions.