Preprint Article Version 1 This version is not peer-reviewed

Multifarious Results for q-Hermite Based Frobenius Type Eulerian Polynomials

Version 1 : Received: 19 August 2019 / Approved: 20 August 2019 / Online: 20 August 2019 (11:20:12 CEST)

How to cite: Khan, W.; Khan, I.A.; Acikgoz, M.; Duran, U. Multifarious Results for q-Hermite Based Frobenius Type Eulerian Polynomials. Preprints 2019, 2019080215 (doi: 10.20944/preprints201908.0215.v1). Khan, W.; Khan, I.A.; Acikgoz, M.; Duran, U. Multifarious Results for q-Hermite Based Frobenius Type Eulerian Polynomials. Preprints 2019, 2019080215 (doi: 10.20944/preprints201908.0215.v1).

Abstract

In this paper, a new class of q-Hermite based Frobenius type Eulerian polynomials is introduced by means of generating function and series representation. Several fundamental formulas and recurrence relations for these polynomials are derived via different generating methods. Furthermore, diverse correlations including the q-Apostol-Bernoulli polynomials, the q-Apostol-Euler poynoomials, the q-Apostol-Genocchi polynomials and the q-Stirling numbers of the second kind are also established by means of the their generating functions.

Subject Areas

Hermite polynomials, Frobenius type Eulerian polynomials, Hermite based Frobenius type Eulerian polynomials, q-numbers, q-polynomials.

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