A new proof of the fundamental two-term transformation for the series ${}_3F_2(1)$ due to Thomae

TL;DR

This paper presents a simplified proof of Thomae's fundamental two-term transformation for the hypergeometric series ${}_3F_2(1)$, enhancing understanding of this classical result.

Contribution

It introduces a straightforward proof of Thomae's transformation, making this important result more accessible and easier to understand.

Findings

Simplified proof of Thomae's two-term transformation

Clarification of the underlying structure of ${}_3F_2(1)$ transformations

Enhanced accessibility for researchers studying hypergeometric functions

Abstract

The aim of this short note is to provide a very simple proof for obtaining the fundamental two-term transformation for the series ${}_3F_2(1)$ due to Thomae.