Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Notes on $q$-Hermite Based Unified Apostol Type Polynomials

Version 1 : Received: 6 May 2019 / Approved: 7 May 2019 / Online: 7 May 2019 (11:20:54 CEST)

How to cite: Khan, W. Notes on $q$-Hermite Based Unified Apostol Type Polynomials. Preprints 2019, 2019050077 (doi: 10.20944/preprints201905.0077.v1). Khan, W. Notes on $q$-Hermite Based Unified Apostol Type Polynomials. Preprints 2019, 2019050077 (doi: 10.20944/preprints201905.0077.v1).

## Abstract

In this article, a new class of $q$-Hermite based unified Apostol type polynomials is introduced by means of generating function and series representation. Several important formulas and recurrence relations for these polynomials are derived via different generating methods. We also introduce $q$-analog of Stirling numbers of second kind of order $\nu$ by which we construct a relation including aforementioned polynomials.

## Keywords

$q$-Hermite type polynomials, $q$-unified Apostol type polynomials, $q$-Hermite based unified Apostol type polynomials.

## Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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