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

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Communications in Advanced Mathematical Sciences
Volume: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 NAHİD

Pages : 1-8

Doi:10.33434/cams.475529

View : 34 | Download : 10

Publication Date : 2019-03-22

Article Type : Research Paper

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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