Two identities and closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of the second kind-Reference-Cited by-同舟云学术

Two identities and closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of the second kind

Published:2022-01-01 Issue:1 Volume:55 Page:822-830
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Chen Xue-Yan¹,Wu Lan²,Lim Dongkyu³,Qi Feng⁴⁵

Affiliation:

1. College of Engineering, Key Laboratory of Intelligent Manufacturing Technology, Inner Mongolia Minzu University , Tongliao 028000 , Inner Mongolia , China

2. College of Engineering, Inner Mongolia Minzu University , Tongliao 028000 , Inner Mongolia , China

3. Department of Mathematics Education, Andong National University , Andong 36729 , Republic of Korea

4. Institute of Mathematics, Henan Polytechnic University , Jiaozuo 454003 , China

5. Independent Researcher , Dallas , TX 75252-8024 , USA

Abstract

Abstract In this article, the authors present two identities involving products of the Bernoulli numbers, provide four alternative proofs for these two identities, derive two closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of the second kind, and supply simple proofs of series expansions of (hyperbolic) cosecant and cotangent functions.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/dema-2022-0166/pdf

Reference14 articles.

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3. F. Qi, On signs of certain Toeplitz-Hessenberg determinants whose elements involve Bernoulli numbers, Contrib. Discrete Math. 18 (2023), no. 1, in press.

4. Y. Shuang, B.-N. Guo, and F. Qi, Logarithmic convexity and increasing property of the Bernoulli numbers and their ratios, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 115 (2021), no. 3, Paper No. 135, 12 pages, https://doi.org/10.1007/s13398-021-01071-x.

5. P. L. Butzer, M. Schmidt, E. L. Stark, and L. Vogt, Central factorial numbers; their main properties and some applications, Numer. Funct. Anal. Optim. 10 (1989), no. 5–6, 419–488, https://doi.org/10.1080/01630568908816313.

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