Biomimetic synthesis of ZnO–NPs and their topical application on S. aureus induced skin infection leads to reduction in infection in mice model.

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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 [14] and Pathan et al [29,30]. Keywords:Hermite polynomials, poly-Bernoulli polynomials of the second kind, Hermite poly-Bernoulli polynomials of the second kind, summation formulae, symmetric identities Cite This Article:

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Abstract. In this paper, we introduce a unified family of Laguerre-based Apostol Bernoulli, Euler and Genocchi polynomials and derive some implicit summation formulae and general symmetry identities arising from different analytical means and applying generating functions. The result extend some known summations and identities of generalized Bernoulli, Euler and Genocchi numbers and polynomials.