Some Identities of the Higher-Order Type 2 Bernoulli Numbers and Polynomials of the Second Kind
  • Taekyun Kim1,*, Dae San Kim2, Dmitry V. Dolgy3, Si-Hyeon Lee1, Jongkyum Kwon4,*
1 Department of Mathematics, Kwangwoon University, Seoul, 139-701, Korea
2 Department of Mathematics, Sogang University, Seoul, 121-742, Korea
3 Kwangwoon Glocal Education Center, Kwangwoon University, Seoul, 139-701, Korea
4 Department of Mathematics Education, Gyeongsang National University, Jinju, 52828, Korea
* Corresponding Authors: Taekyun Kim. Email: kimtk2015@gmail.com; Jongkyum Kwon. Email: mathkjk26@gnu.ac.kr
(This article belongs to this Special Issue:Trend Topics in Special Functions and Polynomials: Theory, Methods, Applications and Modeling)
Received 17 March 2021; Accepted 10 May 2021 ; Published online 08 July 2021
Abstract
We introduce the higher-order type 2 Bernoulli numbers and polynomials of the second kind. In this paper, we investigate some identities and properties for them in connection with central factorial numbers of the second kind and the higher-order type 2 Bernoulli polynomials. We give some relations between the higher-order type 2 Bernoulli numbers of the second kind and their conjugates.
Keywords
Bernoulli polynomials of the second kind; higher-order type 2 Bernoulli polynomials of the second kind; higher-order conjugate type 2 Bernoulli polynomials of the second kind