No abstract

In this paper, we introduce a new class of degenerate Hermite poly-Bernoulli polynomials with q-parameter and give some identities of these polynomials related to the Stirling numbers of the second kind. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions. These results extend some known summations and identities of degenerate Hermite poly-Bernoulli numbers and polynomials.Mathematics Subject Classification (2010): 11B68, 11B73, 11B75, 33C45.

ABSTRACT. This paper extends the Meijer transformation, M, given by

The intent of the paper is to establish some interesting integrals involving the product of generalized Bessel-Maitland function with Jacobi polynomial, which are expressed in terms of generalized hypergeometric function. Some special cases are deduced.

In this paper, we introduce the Hermite-based poly-Bernoulli numbers and polynomials with q-parameter and give some of their basic properties including not only addition property, but also derivative properties and integral representations. We also define the Hermitebased λ-Stirling polynomials of the second kind and then provide some relations, identities of these polynomials related to the Stirling numbers of the second kind. We derive some symmetric identities for these families of special functions by applying the generating functions.