eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2015-12-05 3 5 120 125 10.12691/tjant-3-5-2 TJANT2015352 article Waseem A. Khan waseem08_khan@rediffmail.com 1 N. U. Khan 2 Sarvat Zia 2 Department of Mathematics, Integral University, Lucknow-226026, India Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh, India 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]. http://pubs.sciepub.com/tjant/3/5/2/tjant-3-5-2.pdf Hermite polynomials poly-Bernoulli polynomials of the second kind Hermite poly-Bernoulli polynomials of the second kind summation formulae symmetric identities