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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  and Pathan et al [29, 30] . Keywords: Hermite polynomials,doi:10.12691/tjant-3-5-2 fatcat:iz4mb74ftzcwpdrgyzmye7en6m