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

Ugur Duran; Mehmet Acikgoz; Serkan Araci

doi:10.20944/preprints202006.0355.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

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.

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

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

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