Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Some Properties of the Generalized Apostol Type Hermite-Based Polynomials

  • Received : 2014.11.10
  • Accepted : 2015.05.13
  • Published : 2015.09.23
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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.

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  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