The Airy transform and associated polynomials

• Authors: Danilo Babusci , Giuseppe Dattoli , Dario Sacchetti
• Languages of publication: EN

Abstracts

EN

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

EN

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

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2011
• Volume: 9
• Issue: 6
• Pages: 1381-1386

Dates

published

1 - 12 - 2011

online

15 - 10 - 2011

Contributors

author

Danilo Babusci

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

author

Giuseppe Dattoli

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

author

Dario Sacchetti

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

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Identifiers

DOI

10.2478/s11534-011-0057-9