Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

A Novel Kind of the Type 2 Poly-Fubini Polynomials and Numbers

Version 1 : Received: 23 September 2020 / Approved: 24 September 2020 / Online: 24 September 2020 (11:35:42 CEST)

How to cite: Khan, W. A Novel Kind of the Type 2 Poly-Fubini Polynomials and Numbers. Preprints 2020, 2020090581 (doi: 10.20944/preprints202009.0581.v1). Khan, W. A Novel Kind of the Type 2 Poly-Fubini Polynomials and Numbers. Preprints 2020, 2020090581 (doi: 10.20944/preprints202009.0581.v1).

Abstract

Motivation by the definition of the type 2 poly-Bernoulli polynomials introduced by Kim-Kim [9], in the present paper, we consider a new class of new generating function for the Fubini polynomials, called the type 2 poly-Fubini polynomials by means of the polyexponential function. Then, we derive some useful relations and properties. We show that the type 2 poly-Fubini polynomials equal a linear combination of the classical of the Fubini polynomials and Stirling numbers of the first kind. In a special case, we give a relation between the type 2 poly-Fubini polynomials and Bernoulli polynomials of order r. Moreover, inspired by the definition of the unipoly-Bernoulli polynomials introduced by Kim-Kim [9]. We introduce the type 2 unipoly-Fubini polynomials by means of unipoly function and give multifarious properties including derivative and integral properties. Furthermore, we provide a correlation between the unipoly-Fubini polynomials and the classical Fubini polynomials.

Subject Areas

Polyexponential functions, type 2 poly-Fubini polynomials, unipoly functions.

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