Article ID: MTJPAM-D-25-00070

Title: New identities for generalized Fubini polynomials and moments of geometric distribution


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

Article ID: MTJPAM-D-25-00070; Volume 7 / Issue 4 / Year 2025, Pages 1-15

Document Type: Research Paper

Author(s): Neslihan Kilar a

aDepartment of Computer Technologies, Bor Vocational School, Niğde Ömer Halisdemir University, TR-51700 Niğde, Turkey

Received: 10 March 2025, Accepted: 30 May 2025, Published: 30 December 2025

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

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Abstract

This paper aims to investigate the generalized Fubini polynomials, which are members of the Appell polynomials, and their fundamental properties. By using the generating function of these polynomials, many identities, derivative formulas, and integral formulas are derived, related to some special polynomials and numbers, including the Stirling numbers, Fubini type polynomials, Euler type polynomials, and Bernoulli type polynomials. Furthermore, some formulas involving these polynomials and moments of geometric random variables are presented. These results not only relationships between the generalized Fubini polynomials and their applications but also enhance our understanding of their structure within the Appell polynomials. Moreover, these results provide a foundation for future studies in number theory and mathematical analysis.

Keywords: Generalized Fubini polynomials, Stirling numbers, Bernoulli numbers and polynomials, Euler numbers and polynomials, geometric distribution and moments

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Cite this article

How to cite this article: N. Kilar, New identities for generalized Fubini polynomials and moments of geometric distribution, Montes Taurus J. Pure Appl. Math. 7 (4), 1-15, 2025; Article ID: MTJPAM-D-25-00070.