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Open Physics

formerly Central European Journal of Physics

Editor-in-Chief: Feng, Jonathan

Managing Editor: Lesna-Szreter, Paulina

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Volume 9, Issue 6 (Dec 2011)


The Airy transform and associated polynomials

Danilo Babusci / Giuseppe Dattoli / Dario Sacchetti
  • Dipartimento di Statistica Probabilità e Statistica Applicata, Università “Sapienza”, P.le A. Moro, 5, 00185, Roma, Italy
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Published Online: 2011-10-15 | DOI: https://doi.org/10.2478/s11534-011-0057-9


The Airy transform is an ideally suited tool to treat problems in classical and quantum optics. Even though the relevant mathematical aspects have been thoroughly investigated, the possibilities it offers are wide and some features, such as the link with special functions and polynomials, still contain unexplored aspects. In this note we will show that the so called Airy polynomials are essentially the third order Hermite polynomials. We will also prove that this identification opens the possibility of developing new conjectures on the properties of this family of polynomials.

Keywords: Airy transform; Airy polynomials; Hermite polynomials; Schrödinger-type equation

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About the article

Published Online: 2011-10-15

Published in Print: 2011-12-01

Citation Information: Open Physics, ISSN (Online) 2391-5471, DOI: https://doi.org/10.2478/s11534-011-0057-9.

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© 2011 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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