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http://dx.doi.org/10.5666/KMJ.2015.55.3.597

Some Properties of the Generalized Apostol Type Hermite-Based Polynomials  

KHAN, WASEEM AHMAD (Department of Mathematics, Integral University)
Publication Information
Kyungpook Mathematical Journal / v.55, no.3, 2015 , pp. 597-614 More about this Journal
Abstract
In this paper, we study some properties of the generalized Apostol type Hermite-based polynomials. which extend some known results. We also deduce some properties of the generalized Apostol-Bernoulli polynomials, the generalized Apostol-Euler polynomials and the generalized Apostol-Genocchi polynomials of high order. Numerous properties of these polynomials and some relationships between $F_n{^{({\alpha})}}(x;{\lambda};{\mu};{\nu};c)$ and $_HF_n{^{({\alpha})}}(x;{\lambda};{\mu};{\nu};c)$ are established. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions.
Keywords
Hermite polynomials; generalized Apostol type Hermite-based polynomials; summation formulae;
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