Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

A New Family of Frobenius-Genocchi Polynomials and Its Certain Properties

Version 1 : Received: 3 July 2020 / Approved: 5 July 2020 / Online: 5 July 2020 (06:47:53 CEST)
Version 2 : Received: 2 October 2020 / Approved: 2 October 2020 / Online: 2 October 2020 (13:58:25 CEST)

How to cite: Duran, U.; Acikgoz, M.; Araci, S. A New Family of Frobenius-Genocchi Polynomials and Its Certain Properties. Preprints 2020, 2020070048 (doi: 10.20944/preprints202007.0048.v2). Duran, U.; Acikgoz, M.; Araci, S. A New Family of Frobenius-Genocchi Polynomials and Its Certain Properties. Preprints 2020, 2020070048 (doi: 10.20944/preprints202007.0048.v2).

Abstract

Recently, Kim-Kim [13] have introduced polyexponential functions as an inverse to the polylogarithm functions, and constructed type 2 poly-Bernoulli polynomials. They have also introduced unipoly functions attached to each suitable arithmetic function as a universal concept. Inspired by their work, in this paper, we introduce a new class of the Frobenius-Genocchi polynomials. We derive the diverse formulas and identities covering some summation formulas, derivative formula and correlations with Bernoulli polynomials and numbers, Stirling numbers of the both kinds, degenerate Frobenius-Genocchi polynomials and degenerate Frobenius-Euler polynomials. Moreover, by using the unipoly function as following Kim-Kim's work in <cite>Kim1</cite>, we consider degenerate unipoly-Frobenius-Genocchi polynomials and investigate some formulas and relationships with Daehee numbers, degenerate Frobenius-Genocchi numbers and Stirling numbers of the first kind. Finally, we obtain an Gaussian integral representation of the Frobenius-Genocchi polynomials in terms of the 2-variable Hermite polynomials.

Subject Areas

Polyexponential function; Degenerate exponential function; Polyexponential function; Frobenius-Genocchi polynomials; Poly-Frobenius-Genocchi polynomials

Comments (1)

Comment 1
Received: 2 October 2020
Commenter: Ugur Duran
Commenter's Conflict of Interests: Author
Comment: We revised our paper and all corrections were done.
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