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Open AccessArticle

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

Department of Mathematics, Faculty of Science, University of Akdeniz, TR-07058 Antalya, Turkey
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Symmetry 2019, 11(9), 1097; https://doi.org/10.3390/sym11091097
Received: 27 July 2019 / Revised: 15 August 2019 / Accepted: 16 August 2019 / Published: 2 September 2019
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. View Full-Text
Keywords: Apostol-type numbers and polynomials; Stirling numbers; combinatorial sum; generating function; special functions Apostol-type numbers and polynomials; Stirling numbers; combinatorial sum; generating function; special functions
MDPI and ACS Style

Kilar, N.; Simsek, Y. Two Parametric Kinds of Eulerian-Type Polynomials Associated with Euler’s Formula. Symmetry 2019, 11, 1097.

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