Verification of Binomial theorem and Chu-Vandermonde convolution by the finite difference method

TL;DR

This paper demonstrates that the Binomial theorem and Chu-Vandermonde convolution can be verified using the finite difference method, providing a novel approach to their proof.

Contribution

It introduces a new verification technique for these classical combinatorial identities using finite difference methods.

Findings

Verification of Binomial theorem via finite differences

Verification of Chu-Vandermonde convolution via finite differences

Provides a new perspective on classical combinatorial identities

Abstract

In this note, we show that Binomial theorem and Chu-Vandermonde convolution can both be verified by the finite difference method.