Preprint Article Version 1 This version is not peer-reviewed

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 (doi: 10.20944/preprints201807.0352.v1). Khan, W.A.; Nisar, K. Some New Classes of Generalized Lagrange-Based Apostol Type Hermite Polynomials. Preprints 2018, 2018070352 (doi: 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.

Subject Areas

Hermite polynomials; Chan-Chyan-Srivastava polynomials; lagrange-based apostol type Hermite polynomials; summation formulae; symmetric identities

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