Work

Extensions of several famous combinatorial identities via hypergeometric functions

Year: 2026

Type: preprint

Abstract: The objective of this paper is to develop an extension of Kummer's second theorem and to establish generalized forms of four classical combinatorial identities---Knuth's old sum (also known as Reed--Dawson's combinatorial identity), Riordan's combinatorial identity, Gould's combinatorial identity, and Touchard's combinatorial identity---using a hypergeometric-series approach. Several new identities also arise as special cases of our main results.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.05192

Authors: Rathie, Arjun Kumar, Qi, Feng, Lim, Dongkyu

Institutions: Gyeongkuk National University, Rajasthan Technical University, Hulunbuir University

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7201843739

Cites: 15

Cited by:

Related to: 10