Some Properties of the Generalized Apostol Type Hermite- Based Polynomials
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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. Numer- ous properties of these polynomials and some relationships between F(α) n (x, λ, μ, v, c) and HF(α) n (x, y, λ, μ, v, c) are established. Some implicit summation formulae and general sym- metry identities are derived by using di®erent analytical means and applying generating functions.
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. Numer- ous properties of these polynomials and some relationships between F(α) n (x, λ, μ, v, c) and HF(α) n (x, y, λ, μ, v, c) are established. Some implicit summation formulae and general sym- metry identities are derived by using di®erent analytical means and applying generating functions.
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