Preprint Article Version 1 This version is not peer-reviewed

Some Properties of $Q$-Hermite Fubini Numbers and Polynomials

Version 1 : Received: 26 April 2019 / Approved: 28 April 2019 / Online: 28 April 2019 (10:15:26 CEST)

How to cite: Khan, W.A. Some Properties of $Q$-Hermite Fubini Numbers and Polynomials. Preprints 2019, 2019040309 (doi: 10.20944/preprints201904.0309.v1). Khan, W.A. Some Properties of $Q$-Hermite Fubini Numbers and Polynomials. Preprints 2019, 2019040309 (doi: 10.20944/preprints201904.0309.v1).

Abstract

The main purpose of this paper is to introduce a new class of $q$-Hermite-Fubini numbers and polynomials by combining the $q$-Hermite polynomials and $q$-Fubini polynomials. By using generating functions for these numbers and polynomials, we derive some alternative summation formulas including powers of consecutive $q$-integers.  Also, we establish some relationships for $q$-Hermite-Fubini polynomials associated with $q$-Bernoulli polynomials, $q$-Euler polynomials and $q$-Genocchi polynomials and $q$-Stirling numbers of the second kind.

Subject Areas

$q$-Hermite polynomials; $q$-Hermite-Fubini polynomials; $q$-Bernoulli polynomials; $q$-Euler polynomials; $q$-Genocchi polynomials; Stirling numbers of the second kind

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