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Research Article | Open Access

Combinatorial identities concerning trigonometric functions and Fibonacci/Lucas numbers

Yulei Chen1, Yingming Zhu2, Dongwei Guo2( )
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou (Henan), China
School of Economics and Management, Nanjing University of Science and Technology, Nanjing (Jiangsu), China
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Abstract

In this work, by means of the generating function method and the De Moivre's formula, we derive some interesting combinatorial identities concerning trigonometric functions and Fibonacci/Lucas numbers. One of them confirms the formula proposed recently by Svinin (2022).

Keywords

Fibonacci numbersLucas numbersbinomial coefficientstrigonometric functions
CLC number: 05A19, 11B65

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AIMS Mathematics
Volume 9 Issue 4,
April 2024
Pages 9348-9363
DOI: 10.3934/math.2024455

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Cite this article:
Chen Y, Zhu Y, Guo D. Combinatorial identities concerning trigonometric functions and Fibonacci/Lucas numbers. AIMS Mathematics, 2024, 9(4): 9348-9363. https://doi.org/10.3934/math.2024455

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Received: 29 December 2023
Revised: 29 February 2024
Accepted: 05 March 2024
Published: 15 April 2024
©2024 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)