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Research Article | Open Access

The binomial sums for four types of polynomials involving floor and ceiling functions

Qingjie Chai1,2, Hanyu Wei2( )
School of Mathematics and Statistics, Henan Normal University, Xinxiang 453007, China
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
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Abstract

Several binomial sums are established for the Pell polynomials and the Pell-Lucas polynomials, as well as two types of the Chebyshev polynomials and the Fibonacci-Lucas numbers, which include two special cases proposed by Hideyuki Othsuka in 2024.

Keywords

the binomial theoremPell polynomialsPell-Lucas polynomialsthe first kind of Chebyshev polynomialsthe second kind of Chebyshev polynomials

References

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Electronic Research Archive
Volume 33 Issue 3,
March 2025
Pages 1384-1397
DOI: 10.3934/era.2025064

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Cite this article:
Chai Q, Wei H. The binomial sums for four types of polynomials involving floor and ceiling functions. Electronic Research Archive, 2025, 33(3): 1384-1397. https://doi.org/10.3934/era.2025064

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Received: 16 December 2024
Revised: 20 February 2025
Accepted: 21 February 2025
Published: 15 March 2025
©2025 the Author(s), licensee AIMS Press.

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