Product formulas for hypergeometric functions over finite fields

TL;DR

This paper develops new product formulas for hypergeometric functions defined over finite fields, extending classical identities from complex analysis to finite field settings.

Contribution

It introduces analogous product formulas for hypergeometric functions over finite fields, a novel extension of classical identities.

Findings

Established new product formulas for finite field hypergeometric functions

Extended classical identities from complex to finite field contexts

Provided foundational results for further research in finite field hypergeometric functions

Abstract

Many product formulas are known classically for generalized hypergeometric functions over the complex numbers. In this paper, we establish some analogous formulas for generalized hypergeometric functions over finite fields.