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Multiple-poly-Bernoulli polynomials of the second kind associated with Hermite polynomials

Khan W. A., Ghayasuddin M., Shadab M.

Fasciculi Mathematici

2017

Nr 58

97--112

In this paper, we introduce a new class of Hermite multiple-poly-Bernoulli numbers and polynomials of the second kind and investigate some properties for these polynomials. We derive some implicit summation formulae and general symmetry identities by using different analytical means and applying generating functions. The results derived here are a generalization of some known summation formulae earlier studied by Pathan and Khan.

Some new classes of generalized Hermite-Based Apostol-Euler and Apostol-Genocchi polynomials

Pathan M. A., Khan W. A.

Fasciculi Mathematici

2015

Nr 55

153--170

In this paper, we introduce a new class of generalized Apostol-Hermite-Euler polynomials and Apostol-Hermi-te-Genocchi polynomials and derive some implicit summation formulae by applying the generating functions. These results extend some known summations and identities of generalized Hermite-Euler polynomials studied by Dattoli et al, Kurt and Pathan.