A note on a generalization of two well-known Cominatorial identities via a Hypergeometric series approach

TL;DR

This paper generalizes two classical combinatorial identities by employing a hypergeometric series approach, offering a broader understanding of these identities and their potential applications.

Contribution

It introduces a unified hypergeometric series framework to generalize Knuth's sum and Riordan's identity, expanding their scope and applicability.

Findings

Generalized Knuth's sum using hypergeometric series

Extended Riordan's identity through a hypergeometric approach

Provided new identities that encompass classical results

Abstract

In this note, we aim to provide generalizations of (i) Knuth's old sum (or Reed Dawson identity) and (ii) Riordan's identity using a hypergeometric series approach.