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Pathan, M.A and Khan, W.A: Some implicit summation formulas and symmetric identities for the generalized Hermite based- polynomials, Acta Universitatis Apulensis, 39(2014), 113-136.

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

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

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


Turkish Journal of Analysis and Number Theory. 2015, Vol. 3 No. 5, 120-125
DOI: 10.12691/tjant-3-5-2
Copyright © 2015 Science and Education Publishing

Cite this paper:
Waseem A. Khan, N. U. Khan, 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.

Correspondence to: Waseem  A. Khan, Department of Mathematics, Integral University, Lucknow-226026, India. Email: waseem08_khan@rediffmail.com

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].

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