# Some Properties of the Generalized Apostol Type Hermite-Based Polynomials

• KHAN, WASEEM AHMAD (Department of Mathematics, Integral University)
• Accepted : 2015.05.13
• Published : 2015.09.23
• 55 5

#### 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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#### Cited by

1. A new generalization of Apostol type Hermite–Genocchi polynomials and its applications vol.5, pp.1, 2016, https://doi.org/10.1186/s40064-016-2357-4