Combinatorial identities concerning trigonometric functions and Fibonacci/Lucas numbers

被引：1

作者：

Chen, Yulei ^{[1
]}

Zhu, Yingming ^{[2
]}

Guo, Dongwei ^{[2
]}

机构：

[1] Zhoukou Normal Univ, Sch Math & Stat, Zhoukou, Henan, Peoples R China

[2] Nanjing Univ Sci & Technol, Sch Econ & Management, Nanjing, Jiangsu, Peoples R China

来源：

AIMS MATHEMATICS | 2024年 / 9卷 / 04期

关键词：

Fibonacci numbers; Lucas numbers; binomial coefficients; trigonometric functions;

D O I：

10.3934/math.2024455

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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).

引用

页码：9348 / 9363

页数：16

共 50 条

[31] MORE IDENTITIES AND TRIDIAGONAL MATRICES ABOUT FIBONACCI AND LUCAS NUMBERS
Feng, Jishe
[J]. ARS COMBINATORIA, 2013, 108 : 269 - 277
[32] New identities involving generalized Fibonacci and generalized Lucas numbers
Abd-Elhameed, W. M.
Zeyada, N. A.
[J]. INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2018, 49 (03): : 527 - 537
[33] Tiling approach to obtain identities for generalized Fibonacci and Lucas numbers
Belbachir, Hacene
Belkhir, Amine
[J]. ANNALES MATHEMATICAE ET INFORMATICAE, 2013, 41 : 13 - 17
[34] Some reciprocal summation identities with applications to the Fibonacci and Lucas numbers
Jennings, D
[J]. APPLICATIONS OF FIBONACCI NUMBERS, VOL 7, 1998, : 197 - 200
[35] Fractional-power identities for Fibonacci and Lucas polynomials and numbers
Gauthier, N.
[J]. MATHEMATICAL GAZETTE, 2011, 95 (534): : 486 - 494
[36] Families of identities involving sums of powers of the Fibonacci and Lucas numbers
Melham, RS
[J]. FIBONACCI QUARTERLY, 1999, 37 (04): : 315 - 319
[37] Identities for combinatorial sums involving trigonometric functions
Alzer, H.
Yakubovich, S.
[J]. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2023, 34 (08) : 563 - 569
[38] THE USE OF CRAGMONT FIBONACCI MATRICES IN ANALYZING AND CATALOGING IDENTITIES WITH POWERS OF FIBONACCI AND LUCAS NUMBERS
Hisert, George A.
[J]. JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2019, 41 (01): : 95 - 119
[39] ON SOME COMBINATORIAL IDENTITIES INVOLVING THE TERMS OF GENERALIZED FIBONACCI AND LUCAS SEQUENCES
Akyuz, Zeynep
Halici, Serpil
[J]. HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2013, 42 (04): : 431 - 435
[40] Fibonacci and Lucas Numbers of Factorials and Factorials of Fibonacci and Lucas
Phunphayap, Phakhinkon
Khemaratchatakumthorn, Tammatada
Sumritnorrapong, Patcharee
[J]. INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2022, 17 (01): : 11 - 19

← 1 2 3 4 5 →