- Communications in Advanced Mathematical Sciences
- Vol: 2 Issue: 1
- A Unified Family of Generalized $q$-Hermite Apostol Type Polynomials and its Applications
A Unified Family of Generalized $q$-Hermite Apostol Type Polynomials and its Applications
Authors : Subuhi Khan, Tabinda Nahid
Pages : 1-8
Doi:10.33434/cams.475529
View : 11 | Download : 8
Publication Date : 2019-03-22
Article Type : Research
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