Triple Symmetric Sums of Circular Binomial Products

Author:

Chen Marta Na1ORCID,Chu Wenchang2ORCID

Affiliation:

1. School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China

2. Department of Mathematics and Physics, University of Salento, 73100 Lecce, Italy

Abstract

By employing the generating function approach, 16 triple sums for circular binomial products of binomial coefficients are examined. Recurrence relations and generating functions are explicitly determined. These symmetric sums may find potential applications in the analysis of algorithms, symbolic calculus, and computations in theoretical physics.

Publisher

MDPI AG

Reference22 articles.

1. Binomial sum relations involving Fibonacci and Lucas numbers;Adegoke;Appl. Math.,2023

2. Egorychev, G.P. (1977). Integral Representations and the Computation of Combinatorial Sums, “Nauka” Sibirsk, Otdel.. Translations of Mathematical Monographs 59, Amer. Math. Soc., Providence, R. I. 1984.

3. Graham, R.L., Knuth, D.E., and Patashnik, O. (1989). Concrete Mathematics, Addison–Wesley Publishing Company.

4. Riordan, J. (1968). Combinatorial Identities, John Wiley & Sons.

5. Benjamin, A.T., and Quinn, J.J. (2003). Proofs That Really Count: The Art of Combinatorial Proof, The Dolciani Mathematical Expositions, Mathematical Association of America.

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