A note on the (p,q)-Hermite polynomials
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CitationDuran, U., Acikgoz, M., Esi, A., Araci, S. ( January, 1, 2018) . A note on the (p,q)-Hermite polynomials, Applied Mathematics and Information Sciences. 12, 1, 227-231.
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.