Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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. https://doi.org/10.20944/preprints201904.0309.v1 Khan, W.A. Some Properties of $Q$-Hermite Fubini Numbers and Polynomials. Preprints 2019, 2019040309. https://doi.org/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.

Keywords

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

Subject

Computer Science and Mathematics, Algebra and Number Theory

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