Unified degenerate Apostol-type Bernoulli, Euler, Genocchi, and Fubini polynomials

Volume 25, Issue 3, pp 259--268 http://dx.doi.org/10.22436/jmcs.025.03.05

Publication Date: July 03, 2021 Submission Date: March 24, 2021 Revision Date: May 17, 2021 Accteptance Date: June 07, 2021

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Authors

Burak Kurt - Department of the Mathematics, Faculty of Education, Akdeniz University, TR-07070 Antalya, Turkey.

Abstract

Recently, Acala in [N. G. Acala, Eur. J. Pure Appl. Math., \(\bf 13\) (2020), 587--607, N. G. Acala, J. Math. Comput. Sci., \(\bf 23\) (2021), 10--25] introduced and investigated the Apostol-type Bernoulli, Euler, Genocchi and Fubini polynomials. Acala gave some identities and symmetric relations for those polynomials. In this paper, we define the unified degenerate Apostol-type Bernoulli, Euler, Genocchi, and Fubini polynomials. We give identities and recurrence relations, symmetric relation, and summation formulas.

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Keywords

• The Apostol-Bernoulli
• Apostol-Euler
• Apostol-Genocchi two-variable Fubini polynomials
• degenerate Bernoulli polynomials
• degenerate Stirling numbers of the second kind
• degenerate unified Apostol-type Bernoulli
• Euler, Genocchi, and Fubini polynomials

MSC

•  11B73
•  11B68
•  05A10
•  11B65

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