**Title:** Families of unified and modified presentation of Fubini numbers and polynomials

**Montes Taurus J. Pure Appl. Math.** / ISSN: 2687-4814

**Article ID:** MTJPAM-D-22-00025; **Volume 5 / Issue 1 / Year 2023**, Pages 1-21

**Document Type:** Research Paper

**Author(s):** Neslihan Kilar ^{a} , Yilmaz Simsek ^{b}

^{a}Department of Computer Technologies, Bor Vocational School, Niğde Ömer Halisdemir University, TR-51700 Niğde, Turkey

^{b}Department of Mathematics, Faculty of Science, University of Akdeniz, TR-07058 Antalya, Turkey

Received: 15 August 2022, Accepted: 14 November 2022, Published: 17 December 2022.

**Corresponding Author:** Neslihan Kilar (Email address: neslihankilar@ohu.edu.tr; neslihankilar@gmail.com)

**Full Text:** PDF

**Abstract**

The goal of this paper is to define new families of unified and modified presentation of the Fubini numbers and polynomials with their generating functions. Using generating functions and their functional equations, many properties of these polynomials and numbers are presented. Relations among unified and modified presentation of the Fubini numbers and polynomials, Stirling type numbers, combinatorial type polynomials, and unified presentation of the generalized Bernoulli, Euler and Genocchi polynomials are given. Many novel identities and relations including these polynomials and numbers are also given. Moreover, new Hurwitz-Lerch type zeta functions, which interpolate unified and modified presentation of the Fubini numbers and polynomials at negative integers, are defined. Furthermore, suitable links of identities and relations, which are found in this paper, with those in earlier and future studies are indicated.

**Keywords:** Apostol type numbers and polynomials, combinatorial type numbers, Fubini type numbers and polynomials, generalized Apostol type numbers and polynomials, Stirling type numbers, special numbers, generating function

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