A Probabilistic Approach to Frobenius-Genocchi Polynomials Derived From Polyexponential Function Associated With Their Certain Applications

Ayşe Karagenç; Mehmet Açıkgöz; Serkan Aracı

doi:10.62298/advmath.31

Authors

Ayşe Karagenç Department of Information Security Technology, Faculty of Computer and Information Technologies, Cappadocia University, Nevşehir, Türkiye https://orcid.org/0009-0003-3186-2578
Mehmet Açıkgöz Department of Mathematics, Faculty of Science and Arts, Gaziantep University, TR-27310, Gaziantep, Türkiye https://orcid.org/0000-0003-1091-9697
Serkan Aracı Department of Computer Engineering, Faculty of Engineering, Hasan Kalyoncu University, TR-27010, Gaziantep, Türkiye https://orcid.org/0000-0002-3950-6864

DOI:

https://doi.org/10.62298/advmath.31

Keywords:

Moment generating function, Probabilisitic Frobenius-Genocchi polynomials, Polyexponential-Frobenius-Genocchi polynomials, Random variables

Abstract

In this paper, we introduce probabilistic extensions of polyexponential-Frobenius-Genocchi polynomials. By making use of their generating functions, we derive new and interesting identities among aforementioned polynomials and probabilistic Frobenius-Euler polynomials, the Stirling numbers of the first and second kinds, probabilistic Frobenius-Genocchi polynomials, Bernoulli polynomials of the second kinds, Daehee polynomials, polyexponential probabilistic Bernoulli and polyexponential probabilistic Genocchi polynomials. In special cases, the obtained results reduce to the classical ones. Additionally, by picking suitable random variables, we also obtain new relations involving the Stirling numbers of the first and second kinds, and the Frobenius-Euler numbers.

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A Probabilistic Approach to Frobenius-Genocchi Polynomials Derived From Polyexponential Function Associated With Their Certain Applications

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