Submitted:
19 August 2019
Posted:
20 August 2019
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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.
Keywords:
Hermite polynomials
; Frobenius type Eulerian polynomials
; Hermite based Frobenius type Eulerian polynomials
; q-numbers
; q-polynomials.
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