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

Mahouton Norbert Hounkonnou; Sama Arjika; Won Sang Chung

doi:10.55937/sut/1439291945

June 2015 New families of

q

and

(q;p)

−Hermite polynomials

Mahouton Norbert Hounkonnou, Sama Arjika, Won Sang Chung

Author Affiliations +

SUT J. Math. 51(1): 11-29 (June 2015). DOI: 10.55937/sut/1439291945

Abstract

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, ${\cal L}_n ( \cdot , \cdot |q),$ which appear to be connected with well known $(q,n)$ −exponential functions $E_{q,n} ( \cdot )$ 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.

Funding Statement

MNH and SA acknowledge the Abdus Salam International Centre for Theoretical Physics (ICTP, Trieste, Italy) for its support through the Office of External Activities (OEA) - Prj-15. The ICMPA is also in partnership with the Daniel Iagolnitzer Foundation (DIF), France. One of us (W. S. Chung) was supported by the Gyeongsang National University Fund for Professors on Sabbatical Leave, 2006

Acknowledgements

MNH thanks Professor Tudor Ratiu and his collaborators for their hospitality during his stay as Visiting Professor at the Centre Interfacultaire Bernoulli (CIB) at the Ecole Polytechnique Federale de Lausanne (EPFL) where this work was completed. The authors thank the anonymous referees for their comments and careful reading of the manuscript.

Citation

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Mahouton Norbert Hounkonnou. Sama Arjika. Won Sang Chung. "New families of $q$ and $(q;p)$ −Hermite polynomials." SUT J. Math. 51 (1) 11 - 29, June 2015. https://doi.org/10.55937/sut/1439291945