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Article

Bell-Based Bernoulli Polynomials with Applications

1
Department of Basic Sciences of Engineering, Faculty of Engineering and Natural Sciences, Iskenderun Technical University, TR-31200 Hatay, Turkey
2
Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, TR-27410 Gaziantep, Turkey
3
Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, TR-27310 Gaziantep, Turkey
*
Author to whom correspondence should be addressed.
Academic Editor: Clemente Cesarano
Received: 5 February 2021 / Revised: 23 February 2021 / Accepted: 24 February 2021 / Published: 2 March 2021
(This article belongs to the Special Issue p-adic Analysis and q-Calculus with Their Applications)
In this paper, we consider Bell-based Stirling polynomials of the second kind and derive some useful relations and properties including some summation formulas related to the Bell polynomials and Stirling numbers of the second kind. Then, we introduce Bell-based Bernoulli polynomials of order α and investigate multifarious correlations and formulas including some summation formulas and derivative properties. Also, we acquire diverse implicit summation formulas and symmetric identities for Bell-based Bernoulli polynomials of order α. Moreover, we attain several interesting formulas of Bell-based Bernoulli polynomials of order α arising from umbral calculus. View Full-Text
Keywords: Bernoulli polynomials; bell polynomials; mixed-type polynomials; stirling numbers of the second kind; umbral calculus; summation formulas; derivative properties Bernoulli polynomials; bell polynomials; mixed-type polynomials; stirling numbers of the second kind; umbral calculus; summation formulas; derivative properties
MDPI and ACS Style

Duran, U.; Araci, S.; Acikgoz, M. Bell-Based Bernoulli Polynomials with Applications. Axioms 2021, 10, 29. https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010029

AMA Style

Duran U, Araci S, Acikgoz M. Bell-Based Bernoulli Polynomials with Applications. Axioms. 2021; 10(1):29. https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010029

Chicago/Turabian Style

Duran, Ugur, Serkan Araci, and Mehmet Acikgoz. 2021. "Bell-Based Bernoulli Polynomials with Applications" Axioms 10, no. 1: 29. https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010029

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