On a strange evaluation of the hypergeometric series by Gosper. II

TL;DR

This paper introduces a new hypergeometric identity that encompasses existing identities and relates to Gosper's unusual evaluation, advancing understanding of hypergeometric series evaluations.

Contribution

It presents a novel hypergeometric identity that generalizes previous identities and connects to Gosper's unique evaluation method.

Findings

New hypergeometric identity derived

Identity includes known identities as special cases

Links to Gosper's strange evaluation established

Abstract

There are many identities for the hypergeometric series presented in the article "Special values of the hypergeometric series" by Ebisu. In this note, we obtain a new hypergeometric identity, which includes some of these identities as special cases. We notice that this identity closely relates to a strange evaluation by Gosper. Key Words and Phrases: the hypergeometric series, hypergeometric identity.