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Research Article | Open Access

Generating functions for circular sums of binomial products

Marta Na Chen1, Wenchang Chu2( )
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, China; chennamarta@zknu.edu.cn
Via Dalmazio Birago 9/E, Lecce 73100, Italy
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Abstract

By means of the recursive construction method, we examine a class of multiple sums (with a free variable " x") for circular products of binomial coefficients. They are first expressed as coefficients of bivariate rational functions. Then the rational generating functions are determined by deftly employing Knuth's bracket calculus, resultants of polynomials, and Hadamard products of rational functions.

Keywords

generating functionbinomial coefficientcircular sumKnuth's bracket calculusresultant of polynomialsHadamard products of rational functions
CLC number: Primary 11B39, Secondary 05A15, 11B65

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AIMS Mathematics
Volume 10 Issue 12,
December 2025
Pages 28182-28206
DOI: 10.3934/math.20251239

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Cite this article:
Chen MN, Chu W. Generating functions for circular sums of binomial products. AIMS Mathematics, 2025, 10(12): 28182-28206. https://doi.org/10.3934/math.20251239

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Received: 17 August 2025
Revised: 20 November 2025
Accepted: 25 November 2025
Published: 01 December 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)