HERMITE BASED POLY-BERNOULLI POLYNOMIALS WITH A q-PARAMETER
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초록
We introduce the Hermite based poly-Bernoulli polynomi- als with a 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 Hermite based λ-Stirling polynomi- als of the second kind, and then provide some relations. Moreover, we derive several correlations and identities including the Hermite-Kampe de Feriet (or Gould-Hopper) family of polynomials, the Hermite based poly-Bernoulli polynomials with a q parameter and the Hermite based λ-Stirling polynomials of the second kind.
Abstract
We introduce the Hermite based poly-Bernoulli polynomi- als with a 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 Hermite based λ-Stirling polynomi- als of the second kind, and then provide some relations. Moreover, we derive several correlations and identities including the Hermite-Kampe de Feriet (or Gould-Hopper) family of polynomials, the Hermite based poly-Bernoulli polynomials with a q parameter and the Hermite based λ-Stirling polynomials of the second kind.
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