Explicit relations on the degenerate type 2-unified Apostol–Bernoulli, Euler and Genocchi polynomials and numbers

Burak Kurt
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 3, Pages 486–494
DOI: 10.7546/nntdm.2023.29.3.486-494
Full paper (PDF, 207 Kb)

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Authors and affiliations

Burak Kurt
Department of Mathematics and Science Education, Faculty of Education,
Akdeniz University, Antalya TR-07058, Turkey

Abstract

The main aim of this paper is to introduce and investigate the degenerate type 2-unified Apostol–Bernoulli, Euler and Genocchi polynomials by using monomiality principle and operational methods. We give explicit relations and some identities for the degenerate type 2-unified Apostol–Bernoulli, Euler and Genocchi polynomials.

Keywords

• Type 2-Bernoulli, Euler and Genocchi polynomials
• Degenerate Bernoulli, Euler and Genocchi polynomials
• Unified degenerate Apostol–Bernoulli, Euler and Genocchi polynomials
• Monomiality principle
• Multiplicative operators

2020 Mathematics Subject Classification

• 11B68
• 11B83
• 05A10
• 33B11

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Manuscript history

• Received: 18 November 2022
• Revised: 5 June 2023
• Accepted: 19 June 2023
• Online First: 11 July 2023

Copyright information

Ⓒ 2023 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).