A new class of q-Hermite-based Apostol-type polynomials and its applications

Waseem A. Khan and Divesh Srivastava
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 1, Pages 75–85
DOI: 10.7546/nntdm.2020.26.1.75-85
Full paper (PDF, 196 Kb)

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Authors and affiliations

Waseem A. Khan
Department of Mathematics and Natural Sciences
Prince Mohammad Bin Fahd University
P.O Box 1664, Al Khobar 31952, Saudi Arabia

Divesh Srivastava
Department of Mathematics, Faculty of Science
Integral University
Lucknow-226026, India

Abstract

The present article is to introduce a new class of q-Hermite based Apostol-type
polynomials and to investigate their properties and characteristics. In particular, the generating functions, series expression and explicit and recurrence relations for these polynomials are established. We derive some relationships for q-Hermite based Apostol-type polynomials associated with q-Apostol-type Bernoulli polynomials, q-Apostol-type Euler and q-Apostol-type Genocchi polynomials.

Keywords

• q-polynomials
• q-Hermite-based Apostol-type polynomials
• q-recurrence relations

2010 Mathematics Subject Classification

• 05A10
• 05A15
• 11B68
• 16B65
• 33C45

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