Article
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Some New Classes of Generalized Lagrange-Based Apostol Type Hermite Polynomials
Version 1
: Received: 19 July 2018 / Approved: 19 July 2018 / Online: 19 July 2018 (10:14:08 CEST)
How to cite: Khan, W. A.; Nisar, K. Some New Classes of Generalized Lagrange-Based Apostol Type Hermite Polynomials. Preprints 2018, 2018070352. https://doi.org/10.20944/preprints201807.0352.v1 Khan, W. A.; Nisar, K. Some New Classes of Generalized Lagrange-Based Apostol Type Hermite Polynomials. Preprints 2018, 2018070352. https://doi.org/10.20944/preprints201807.0352.v1
Abstract
In this paper, we introduce a general family of Lagrange-based Apostol-type Hermite polynomials thereby unifying the Lagrange-based Apostol Hermite-Bernoulli and the Lagrange-based Apostol Hermite-Genocchi polynomials. We also define Lagrange-based Apostol Hermite-Euler polynomials via the generating function. In terms of these generalizations, we find new and useful relations between the unified family and the Apostol Hermite-Euler polynomials. We also derive their explicit representations and list some basic properties of each of them. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions.
Keywords
Hermite polynomials; Chan-Chyan-Srivastava polynomials; lagrange-based apostol type Hermite polynomials; summation formulae; symmetric identities
Subject
Computer Science and Mathematics, Analysis
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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