Two Parametric Kinds of Eulerian-Type Polynomials Associated with Euler’s Formula

Symmetry

Yilmaz Simsek¹  Neslihan Kilar¹ 

[1] Department of Mathematics, Faculty of Science, University of Akdeniz, TR-07058 Antalya, Turkey;

关键词: Apostol-type numbers and polynomials;    Stirling numbers;    combinatorial sum;    generating function;    special functions;   

DOI  :  10.3390/sym11091097

来源: DOAJ

【 摘 要 】

The purpose of this article is to construct generating functions for new families of special polynomials including two parametric kinds of Eulerian-type polynomials. Some fundamental properties of these functions are given. By using these generating functions and the Euler’s formula, some identities and relations among trigonometric functions, two parametric kinds of Eulerian-type polynomials, Apostol-type polynomials, the Stirling numbers and Fubini-type polynomials are presented. Computational formulae for these polynomials are obtained. Applying a partial derivative operator to these generating functions, some derivative formulae and finite combinatorial sums involving the aforementioned polynomials and numbers are also obtained. In addition, some remarks and observations on these polynomials are given.

【 授权许可】

Unknown