Multiple Sums of Circular Binomial Products

Marta Na Chen and Wenchang Chu ()
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Marta Na Chen: School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
Wenchang Chu: Department of Mathematics and Physics, University of Salento, 73100 Lecce, Italy

Mathematics, 2024, vol. 12, issue 12, 1-15

Abstract: Five classes of multiple sums about circular products of binomial coefficients are investigated. Their generating functions are explicitly expressed as rational functions, with coefficients being Fibonacci and Lucas numbers. This is fulfilled by a novel approach called “recursive construction”, which also permits us to establish, for the circular sums, both generating functions and recurrence relations through the Lagrange expansion formula.

Keywords: binomial coefficient; generating function; Fibonacci number; Lucas number; circular sum (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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