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

Ugur Duran; Mehmet Acikgoz; Ayhan Esi; Serkan Araci

doi:10.20944/preprints201712.0116.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

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 dene 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.

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

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

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