Combinatorial identities concerning trigonometric functions and Fibonacci/Lucas numbers

Yulei Chen; Yingming Zhu; Dongwei Guo; Yulei Chen; Yingming Zhu; Dongwei Guo

doi:10.3934/math.2024455

AIMS Mathematics

2024, Volume 9, Issue 4: 9348-9363. doi: 10.3934/math.2024455

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Research article

Combinatorial identities concerning trigonometric functions and Fibonacci/Lucas numbers

1.
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou (Henan), China
2.
School of Economics and Management, Nanjing University of Science and Technology, Nanjing (Jiangsu), China

Received: 29 December 2023 Revised: 29 February 2024 Accepted: 05 March 2024 Published: 07 March 2024
MSC : 05A19, 11B65

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).
- Fibonacci numbers,
- Lucas numbers,
- binomial coefficients,
- trigonometric functions
Citation: Yulei Chen, Yingming Zhu, Dongwei Guo. Combinatorial identities concerning trigonometric functions and Fibonacci/Lucas numbers[J]. AIMS Mathematics, 2024, 9(4): 9348-9363. doi: 10.3934/math.2024455

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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).

References

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