Article ID: MTJPAM-D-23-00001

Title: Relations among trigonometric functions, Apostol-type numbers and Peters-type Simsek polynomials


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

Article ID: MTJPAM-D-23-00001; Volume 5 / Issue 1 / Year 2023, Pages 90-101

Document Type: Research Paper

Author(s): Damla Gun a

aDepartment of Mathematics, Faculty of Science, Akdeniz University, Antalya, Turkey

Received: 10 February 2023, Accepted: 27 July 2023, Published: 6 September 2023

Corresponding Author: Damla Gun (Email address: damlagun@akdeniz.edu.tr)

Full Text: PDF

Abstract

The main purpose of this paper is to derive some new identities and finite sums involving some trigonometric functions, Apostol-type numbers, the Stirling numbers, and two variable Fibonacci polynomials with the aid of generating functions for the Peters-type Simsek numbers and polynomials. We give finite and infinite series representations containing the Peters-type Simsek numbers and polynomials of the first and second kinds. Using trigonometric functions and generating functions, we obtain some formulas relations among the Apostol Bernoulli numbers and polynomials, the Stirling numbers, and the Peters-type Simsek numbers of the first kind. Finally, we introduce some infinite series computational formulas associated with trigonometric functions, the Peters-type Simsek numbers and polynomials, Fibonacci numbers and polynomials, and the Chebyshev polynomials of the second kind.

Keywords: Apostol type numbers and polynomials, combinatorial numbers and polynomials, Changhee numbers, Humbert polynomials, generating function, Peters-type Simsek numbers of the first kind, special numbers

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