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

Qingjie Chai; Hanyu Wei; Qingjie Chai; Hanyu Wei

doi:10.3934/era.2025064

Electronic Research Archive

2025, Volume 33, Issue 3: 1384-1397. doi: 10.3934/era.2025064

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Research article

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

Qingjie Chai ^1,2,
Hanyu Wei ^{2
,
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1.
School of Mathematics and Statistics, Henan Normal University, Xinxiang 453007, China
2.
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China

Received: 16 December 2024 Revised: 20 February 2025 Accepted: 21 February 2025 Published: 11 March 2025

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.
- the binomial theorem,
- Pell polynomials,
- Pell-Lucas polynomials,
- the first kind of Chebyshev polynomials,
- the second kind of Chebyshev polynomials
Citation: Qingjie Chai, Hanyu Wei. The binomial sums for four types of polynomials involving floor and ceiling functions[J]. Electronic Research Archive, 2025, 33(3): 1384-1397. doi: 10.3934/era.2025064

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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.

References

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