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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 12 > No. 1


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

PP: 227-231
Ugur Duran, Mehmet Acikgoz, Ayhan Esi, Serkan Araci,
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.

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