On a strange evaluation of the hypergeometric series by Gosper

TL;DR

This paper proves a peculiar hypergeometric series identity originally presented by Gosper and generalizes it using contiguity operators, contributing to the understanding of hypergeometric series evaluations.

Contribution

The paper provides a proof of a strange hypergeometric identity by Gosper and introduces its generalization through the use of contiguity operators.

Findings

Proved Gosper's hypergeometric identity.

Derived a generalized form of the identity.

Enhanced understanding of hypergeometric series evaluations.

Abstract

In a series of letters to D.Stanton, R.W.Gosper presented many strange evaluations of hypergeometric series. Recently, we rediscovered one of the strange hypergeometric identities appearing in [Go]. In this paper, we prove this identity and derive its generalization using contiguity operators. Key Words and Phrases: hypergeometric series, strange evaluation, contiguity operator. 2010 Mathematics Subject Classification Numbers: 33C05.