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A Note on the (p, q)-Hermite Polynomials
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: 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
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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