Degenerate Hermite poly-Bernoulli numbers and polynomials with q-parameter

Waseem Ahmad Khan, Idrees Ahmad Khan, Musharraf Ali

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 dierent analytical means and applying generating
functions. These results extend some known summations and identities
of degenerate Hermite poly-Bernoulli numbers and polynomials.


Keywords


Hermite polynomials, degenerate q-poly-Bernoulli polynomi- als, degenerate Hermite q-poly-Bernoulli polynomials, Summation formulae, Symmetric identities.

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DOI: http://dx.doi.org/10.24193/subbmath.2020.1.01

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