A Note on Hermite poly-Bernoulli Numbers and Polynomials of the Second Kind

Waseem A. Khan^1, , N. U. Khan² and Sarvat Zia¹

¹Department of Mathematics, Integral University, Lucknow-226026, India

²Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh, India

Cite this paper:
Waseem A. Khan, N. U. Khan and Sarvat Zia. A Note on Hermite poly-Bernoulli Numbers and Polynomials of the Second Kind. Turkish Journal of Analysis and Number Theory. 2015; 3(5):120-125. doi: 10.12691/tjant-3-5-2

Abstract

In the paper, we introduce a new concept of poly-Bernoulli numbers and polynomials of the second kind which is called Hermite poly-Bernoulli numbers and polynomials of the second kind. We also investigate and analyse its applications in number theory, combinatorics and other fields of mathematics. The results derived here are a generalization of some known summation formulae earlier studied by Jolany et al. [17,18], Dattoli et al [14] and Pathan et al [29,30].

Keywords:
Hermite polynomials poly-Bernoulli polynomials of the second kind Hermite poly-Bernoulli polynomials of the second kind summation formulae symmetric identities

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