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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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).

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Cite this paper

Lim, D. (2023). A note on a generalization of Riordan’s combinatorial identity via a hypergeometric series approach. Notes on Number Theory and Discrete Mathematics, 29(3), 421-425, DOI: 10.7546/nntdm.2023.29.3.421-425.

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