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 deﬁne 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.
Digital Object Identifier (DOI)
Duran, Ugur; Acikgoz, Mehmet; Esi, Ayhan; and Araci, Serkan
"A Note on the (p,q)-Hermite Polynomials,"
Applied Mathematics & Information Sciences: Vol. 12:
1, Article 22.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol12/iss1/22