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. Preprints2020, 2020070048. https://doi.org/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. https://doi.org/10.20944/preprints202007.0048.v2
Duran, U.; Acikgoz, M.; Araci, S. A New Family of Frobenius-Genocchi Polynomials and Its Certain Properties. Preprints2020, 2020070048. https://doi.org/10.20944/preprints202007.0048.v2
APA Style
Duran, U., Acikgoz, M., & Araci, S. (2020). A New Family of Frobenius-Genocchi Polynomials and Its Certain Properties. Preprints. https://doi.org/10.20944/preprints202007.0048.v2
Chicago/Turabian Style
Duran, U., Mehmet Acikgoz and Serkan Araci. 2020 "A New Family of Frobenius-Genocchi Polynomials and Its Certain Properties" Preprints. https://doi.org/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.
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Commenter: Ugur Duran
Commenter's Conflict of Interests: Author