A simple proof of Andrews's 5F4 evaluation

TL;DR

This paper provides a straightforward proof of Andrews's 5F4 hypergeometric series evaluation, utilizing fundamental polynomial principles to simplify the original complex proof.

Contribution

It introduces a simplified proof method for Andrews's 5F4 evaluation based on basic polynomial difference principles, making the proof more accessible.

Findings

The proof confirms Andrews's 5F4 evaluation using elementary polynomial properties.

The approach simplifies understanding of hypergeometric series evaluations.

The method can potentially be applied to similar identities in hypergeometric series.

Abstract

We give a simple proof of George Andrews's balanced 5F4 evaluation using two fundamental principles: the nth difference of a polynomial of degree less than n is zero, and a polynomial of degree n that vanishes at n+1 points is identically zero.