Discrete fractional calculus and the Saalschutz theorem

TL;DR

This paper introduces a new proof of the Saalschutz theorem utilizing discrete fractional calculus and revisits key results like the fractional power rule and Leibniz rule within this framework.

Contribution

It provides a novel proof of the Saalschutz theorem through discrete fractional calculus and reexamines fundamental fractional calculus rules.

Findings

New proof of Saalschutz theorem using discrete fractional calculus

Revisiting fractional power and Leibniz rules within the theory

Enhanced understanding of fractional calculus applications

Abstract

In this work we present a novel proof of the Saalschutz formula by using the theory of discrete fractional calculus. The proofs of some results within this theory, namely, the fractional power rule and the fractional Leibniz rule are revisited.