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ARTICLE

A Note on Bell-Based Bernoulli and Euler Polynomials of Complex Variable

N. Alam¹, W. A. Khan^2,*, S. Obeidat¹, G. Muhiuddin³, N. S. Diab¹, H. N. Zaidi¹, A. Altaleb¹, L. Bachioua¹

1 Department of Basic Sciences, Deanship of Preparatory Year, University of Ha’il, Ha’il, 2440, Saudi Arabia
2 Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar, 31952, Saudi Arabia
3 Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, 71491, Saudi Arabia

* Corresponding Author: W. A. Khan. Email:

(This article belongs to this Special Issue: Algebra, Number Theory, Combinatorics and Their Applications: Mathematical Theory and Computational Modelling)

Computer Modeling in Engineering & Sciences 2023, 135(1), 187-209. https://doi.org/10.32604/cmes.2022.021418

Received 13 January 2022; Accepted 23 May 2022; Issue published 29 September 2022

Abstract

In this article, we construct the generating functions for new families of special polynomials including two parametric kinds of Bell-based Bernoulli and Euler polynomials. Some fundamental properties of these functions are given. By using these generating functions and some identities, relations among trigonometric functions and two parametric kinds of Bell-based Bernoulli and Euler polynomials, Stirling numbers are presented. Computational formulae for these polynomials are obtained. Applying a partial derivative operator to these generating functions, some derivative formulae and finite combinatorial sums involving the aforementioned polynomials and numbers are also obtained. In addition, some remarks and observations on these polynomials are given.

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Keywords

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