Preprint Article Version 1 This version is not peer-reviewed

# Construction of the Type 2 Poly-Frobenius-Genocchi Polynomials with Their Certain Applications

Version 1 : Received: 29 June 2020 / Approved: 30 June 2020 / Online: 30 June 2020 (07:54:52 CEST)

How to cite: Duran, U.; Acikgoz, M.; Araci, S. Construction of the Type 2 Poly-Frobenius-Genocchi Polynomials with Their Certain Applications. Preprints 2020, 2020060355 (doi: 10.20944/preprints202006.0355.v1). Duran, U.; Acikgoz, M.; Araci, S. Construction of the Type 2 Poly-Frobenius-Genocchi Polynomials with Their Certain Applications. Preprints 2020, 2020060355 (doi: 10.20944/preprints202006.0355.v1).

## Abstract

Motivated by the definition of the type 2 poly-Bernoulli polynomials introduced by Kim-Kim, in the present paper, we consider a class of new generating function for the Frobenius-Genocchi polynomials, called the type 2 poly-Frobenius-Genocchi polynomials, by means of the polyexponential function. Then, we derive some useful relations and properties. We show that the type 2 poly-Frobenius-Genocchi polynomias equal a linear combination of the classical Frobenius-Genocchi polynomials and Stirling numbers of the first kind. In a special case, we give a relation between the type 2 poly-Frobenius-Genocchi polynomials and Bernoulli polynomials of order k. Moreover, inspired by the definition of the unipoly-Bernoulli polynomials introduced by Kim-Kim, we introduce the unipoly-Frobenius-Genocchi polynomials by means of unipoly function and give multifarious properties including derivative and integral properties. Furthermore, we provide a correlation between the unipoly-Frobenius-Genocchi polynomials and the classical Frobenius-Genocchi polynomials.

## Subject Areas

Polylogarithm function; Polyexponential function; Frobenius-Genocchi polynomials; Poly-Frobenius-Genocchi polynomials