A Note on Bell-Based Apostol-Type Frobenius-Euler Polynomials of Complex Variable with Its Certain Applications

Noor Alam, Waseem Ahmad Khan and Cheon Seoung Ryoo
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Noor Alam: Department of Basic Sciences, Deanship of Preparatory Year, University of Ha’il, Ha’il 2440, Saudi Arabia
Waseem Ahmad Khan: Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia
Cheon Seoung Ryoo: Department of Mathematics, Hannam University, Daejeon 34430, Korea

Mathematics, 2022, vol. 10, issue 12, 1-26

Abstract: In this paper, we introduce new class of Bell-based Apostol-type Frobenius–Euler polynomials and investigate some properties of these polynomials. We derive some explicit and implicit summation formulas and their symmetric identities by using different analytical means and applying generating functions of generalized Apostol-type Frobenius-Euler polynomials and Bell-based Apostol-type Frobenius-Euler polynomials. In particular, parametric kinds of the Bell-based Apostol-type Frobenius-Euler polynomials are introduced and some of their algebraic and analytical properties are established. In addition, illustrative examples of these families of polynomials are shown, focusing on their numerical values and piloting some beautiful computer-aided graphs of them.

Keywords: Bell polynomials; Apostol-type Frobenius-Euler polynomials; Bell-based Apostol-type Frobenius-Euler polynomials; Stirling numbers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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