Article ID: MTJPAM-D-23-00014

Title: Building generating functions for degenerate Simsek-type numbers and polynomials of higher order


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

Article ID: MTJPAM-D-23-00014; Volume 6 / Issue 3 / Year 2024, Pages 186-198

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 July 2023, Accepted: 1 April 2024, Published: 26 April 2024

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

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Abstract

The objective of this paper is to build generating functions for new families of special numbers and polynomials, which are called higher order degenerate Peters-type Simsek numbers and polynomials of the second kind. Using generating function methods, we give both some fundamental properties of these functions with some relations among the higher order degenerate Peters-type Simsek numbers and polynomials of the second kind, the Stirling numbers of the first kind, the higher order degenerate Changhee numbers and polynomials, and the higher order Apostol-type Daehee numbers and polynomials. We also give some plots of these numbers and polynomials via Wolfram Cloud. Further, applying a partial derivative operator to these generating functions, we obtain derivative formulas for these new families. Eventually, we present further remarks on our new families including their generating functions.

Keywords: Stirling numbers, Apostol-type Daehee numbers and polynomials, degenerate Changhee numbers and polynomials, degenerate Peters-type Simsek numbers and polynomials, generating functions

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Cite this article

How to cite this article: N. Kilar, Building generating functions for degenerate Simsek-type numbers and polynomials of higher order, Montes Taurus J. Pure Appl. Math. 6 (3), 186-198, 2024; Article ID: MTJPAM-D-23-00014.