Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 3 5 2015 12 5 A Note on Hermite poly-Bernoulli Numbers and Polynomials of the Second Kind 120 125 EN Waseem A. Khan Department of Mathematics, Integral University, Lucknow-226026, India N. U. Khan Sarvat Zia TJANT2015352 10.12691/tjant-3-5-2 2015 6 11 2015 10 12 2015 12 3 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].