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formerly Central European Journal of Physics

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The Airy transform and associated polynomials

1Laboratori Nazionali di Frascati, INFN, via E. Fermi 40, I-00044, Frascati, Italy

2Centro Ricerche Frascati, ENEA, via E. Fermi 45, I-00044, Frascati, Italy

3Dipartimento di Statistica Probabilità e Statistica Applicata, Università “Sapienza”, P.le A. Moro, 5, 00185, Roma, Italy

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

Citation Information: Open Physics. Volume 9, Issue 6, Pages 1381–1386, ISSN (Online) 2391-5471, DOI: 10.2478/s11534-011-0057-9, October 2011

Publication History

Published Online:


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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