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

Waseem A. Khan, N. U. Khan, Sarvat Zia
2016 Turkish Journal of Analysis and Number Theory  
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,
more » ... ermite polynomials, poly-Bernoulli polynomials of the second kind, Hermite poly-Bernoulli polynomials of the second kind, summation formulae, symmetric identities Cite This Article:
doi:10.12691/tjant-3-5-2 fatcat:iz4mb74ftzcwpdrgyzmye7en6m