A generalization of Hermite polynomials

Habibullah, G. M.; Shakoor, Abdul

doi:10.12988/imf.2013.13074

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2014

2021

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Cited by 3 publications

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“…The Hermite polynomials are at the bottom of a large class of hypergeometric polynomials to which most of their properties can be generalized [6], [11]- [16]. In [5], Cigler introduced another family of Hermite polynomials H n (x, s) generalizing the physicists and probabilists Hermite polynomials as…”

Section: Introductionmentioning

confidence: 99%

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New families of q and (q;p)-Hermite polynomials

Hounkonnou¹,

Chung²

2014

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In this paper, we construct a new family of q−Hermite polynomials denoted by H n (x, s|q). Main properties and relations are established and proved. In addition, is deduced a sequence of novel polynomials, L n (•, •|q), which appear to be connected with well known (q, n)−exponential functions E q,n (•) introduced by Ernst in his work entitled: A New Method for q−calculus, (Uppsala Dissertations in Mathematics, Vol. 25, 2002). Relevant results spread in the literature are retrieved as particular cases. Fourier integral transforms are explicitly computed and discussed. A (q; p)−extension of the H n (x, s|q) is also provided.

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Section: Introductionmentioning

confidence: 99%

“…. (112)When q goes to 1, x → px and s → p, the polynomials H n,p (x, s|q) become the Hermite polynomials investigated by Habibullah and Shakoor[16], i.e.,H n,p (px, p|1) ≡ S p,n (x) := n! ⌊ n/p ⌋ k=0 (−1) k (px) n−pk k!…”

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confidence: 99%