Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# A Note on the (p, q)-Hermite Polynomials

Version 1 : Received: 16 December 2017 / Approved: 18 December 2017 / Online: 18 December 2017 (08:32:22 CET)

A peer-reviewed article of this Preprint also exists.

Duran, U.; Acikgoz, M.; Esi, A.; Araci, S. A Note on the (p, q)-Hermite Polynomials. Appl. Math. Inf. Sci. 2018, 12 , 227–231. Duran, U.; Acikgoz, M.; Esi, A.; Araci, S. A Note on the (p, q)-Hermite Polynomials. Appl. Math. Inf. Sci. 2018, 12 , 227–231.

## Abstract

In this paper, we introduce a new generalization of the Hermite polynomials via (p, q)-exponential generating function and investigate several properties and relations for mentioned polynomials including derivative property, explicit formula, recurrence relation, integral representation. We also dene a (p, q)-analogue of the Bernstein polynomials and acquire their some formulas. We then provide some (p, q)-hyperbolic representations of the (p, q)-Bernstein polynomials. In addition, we obtain a correlation between (p, q)-Hermite polynomials and (p, q)-Bernstein polynomials.

## Keywords

(p, q)-calculus; hermite polynomials; bernstein polynomials; generating function; hyperbolic functions

Views 0