# Article ID: MTJPAM-D-22-00003

## Title: Formulas for Fubini type numbers and polynomials of negative higher order

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

Article ID: MTJPAM-D-22-00003; Volume 5 / Issue 3 / Year 2023, Pages 23-36

Document Type: Research Paper

Author(s): Neslihan Kilar a

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

Received: 13 February 2022, Accepted: 1 April 2022, Published: 27 May 2022.

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

Full Text: PDF

Abstract

The present paper deals with the Fubini type numbers and polynomials with their generating functions and functional equations. By using these functions, some properties and applications of these polynomials are investigated. Many relations and computation formulas connected with the Stirling type numbers, the Apostol type polynomials and numbers of order -r, the Bernoulli polynomials of order -r, the Euler polynomials and numbers of order -r, the Fubini type numbers and polynomials of order -r and combinatorial numbers are given. Applying the derivative operator to the generating functions of these polynomials, some formulas and combinatorial sums including these numbers and polynomials are also given. Moreover, applying the Riemann integral to some formulas, we derive several interesting finite combinatorial sums associated with the Bernstein basis functions, the Cauchy numbers and the Stirling type numbers.

Keywords: Cauchy numbers, Stirling numbers, Fubini type numbers and polynomials, Bernstein basis functions, combinatorial numbers, special numbers, generating function

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