A note on a generalization of Riordan’s combinatorial identity via a hypergeometric series approach

Dongkyu Lim
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 3, Pages 421–425
DOI: 10.7546/nntdm.2023.29.3.421-425
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Details

Authors and affiliations

Dongkyu Lim
Department of Mathematics Education, Andong National University
Andong 36729, Republic of Korea

Abstract

In this note, an attempt has been made to generalize the well-known and useful Riordan’s combinatorial identity via a hypergeometric series approach.

Keywords

• Combinatorial identity
• Hypergeometric series
• Hypergeometric identities
• Riordan identity
• Reed Dawson identity
• Knuth’s old sum

2020 Mathematics Subject Classification

• Primary: 05A10, 33C20
• Secondary: 40A25

References

1. Andrews, G. E. (1974). Applications of basic hypergeometric functions. SIAM Review, 16(4), 441–484.
2. Choi, J., Rathie, A. K., & Harsh, H. V. (2004). A note on Reed Dawson identities. Korean J. Math. Sciences, 11(2), 1–4.
3. Kim, Y. S., Rathie, A. K., & Paris, R. B. (2018). Evaluations of some terminating series ₂F₁(2) with applications. Turkish Journal of Mathematics, 42(5), 2563–2575.
4. Prodinger, H. (1994). Knuth’s old sum – a survey. EACTS Bulletin, 52, 232–245.
5. Rainville, E. D. (1960). Special Functions. Macmillan Company, New York.
6. Riordan, J. (1971). Combinatorial Identities. John Wiley & Sons, Inc., New York.
7. Roy, R. (1987). Binomial identities and hypergeometric series. The American Mathematical Monthly, 94(1), 36–46.

Manuscript history

• Received: 26 October 2022
• Revised: 25 April 2023
• Accepted: 1 June 2023
• Online First: 6 June 2023

Copyright information

Ⓒ 2023 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).