Research ArticleNo Access

On the new Narayana polynomials, the Gauss Narayana numbers and their polynomials

Engi̇n Özkan

Department of Mathematics, Erzincan Binali Yıldırım University, Faculty of Arts and Sciences, Erzincan, Turkey

E-mail Address: eozkanmath@gmail.com

E-mail Address: eozkan@erzincan.edu.tr

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and

Bahar Kuloğlu

Graduate School of Natural and Applied Sciences, Erzincan Binali Yıldırım University, Erzincan, Turkey

E-mail Address: bahar_kuloglu@hotmail.com

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https://doi.org/10.1142/S179355712150100XCited by:15 (Source: Crossref)

Abstract

We give a new definition of Narayana polynomials and show that there is a relationship between the coefficient of the new Narayana polynomials and Pascal’s triangle. We define the Gauss Narayana numbers and their polynomials. Then we show that there is a relationship between the Gauss Narayana polynomials and the new Narayana polynomials. Also, we show that there is a relationship between the derivatives of the new Narayana polynomials and Pascal’s triangle. We also explain the relationship between the new Narayana polynomials and the known Pell numbers. Finally, we give the Hankel transform of the new Narayana polynomials.

Communicated by I. Inam

Keywords:

AMSC: 11B39, 11B83, 11C08

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