A Unified Family of Generalized $q$-Hermite Apostol Type Polynomials and its Applications

Year 2019, Volume: 2 Issue: 1, 1 - 8, 22.03.2019

Subuhi Khan Tabinda Nahid

https://doi.org/10.33434/cams.475529

Abstract

The intended objective of this paper is to introduce a new class of generalized $q$-Hermite based Apostol type polynomials by combining the $q$-Hermite polynomials and a unified family of $q$-Apostol-type polynomials. The generating function, series definition and several explicit representations for these polynomials are established. The $q$-Hermite-Apostol Bernoulli, $q$-Hermite-Apostol Euler and $q$-Hermite-Apostol Genocchi polynomials are studied as special members of this family and corresponding relations for these polynomials are obtained.

Keywords

$q$-Hermite polynomials, Generalized $q$-Apostol type polynomials, Generalized $q$-Hermite Apostol type polynomials, Explicit representation

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