A simple proof of a generalization of the Chu-Vandermonde identity

TL;DR

This paper presents a straightforward proof of a generalized multivariate Chu-Vandermonde identity, simplifying previous derivations by avoiding complex integral representations and leveraging known properties of special functions.

Contribution

It offers a new, simplified proof of a recent generalization of the multivariate Chu-Vandermonde identity, bypassing the need for Laplace-type integrals.

Findings

Simplified proof of the generalized identity

Avoidance of complex integral representations

Utilization of known properties of Lauricella functions

Abstract

We provide a simple proof of a generalization of the multivariate Chu-Vandermonde identity recently derived in Favaro et al. (2010a). Exploiting known results for rising factorials and fourth Lauricella polynomials we show resorting to Laplace-type integral representation of the fourth Lauricella function may be avoided.