Czasopismo
Tytuł artykułu
Warianty tytułu
Języki publikacji
Abstrakty
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.
Czasopismo
Rocznik
Tom
Numer
Strony
1381-1386
Opis fizyczny
Daty
wydano
2011-12-01
online
2011-10-15
Twórcy
autor
- Laboratori Nazionali di Frascati, INFN, via E. Fermi 40, I-00044, Frascati, Italy, danilo.babusci@lnf.infn.it
autor
- Centro Ricerche Frascati, ENEA, via E. Fermi 45, I-00044, Frascati, Italy, giuseppe.dattoli@enea.it
autor
- Dipartimento di Statistica Probabilità e Statistica Applicata, Università “Sapienza”, P.le A. Moro, 5, 00185, Roma, Italy, dario.sacchetti@uniroma1.it
Bibliografia
- [1] P. Appell, J. Kampé de Fériét, Fonctions Hypergéometriqués Polynôme d’Hermite, (Gauthier-Villars, Paris, 1926)
- [2] G. Dattoli, Appl. Math. Comput. 141, 151 (2003) http://dx.doi.org/10.1016/S0096-3003(02)00329-6[Crossref]
- [3] G. Dattoli, J. Math. Anal. Appl. 284, 447 (2003) http://dx.doi.org/10.1016/S0022-247X(03)00259-2[Crossref]
- [4] K. B. Wolf, Integral Transforms in Science and Engineering, (Plenum Press, New York, 1979)
- [5] A. Horzela, P. Blasiak, G. E. H. Duchamp, K. A. Penson, A. J. Solomon, arXiv:quant-ph/0409152v1
- [6] G. Dattoli, E. Sabia, arXiv:1010.1679v1 [WoS]
- [7] O. Vallée, M. Soares, Airy Functions and application to Physics, (World Scientific, London, 2004)
- [8] D. V. Widder, Am. Math. Mon. 86, 271 (1979) http://dx.doi.org/10.2307/2320744[Crossref]
- [9] M. Feng, Phys. Rev. A 64, 034101 (2001) http://dx.doi.org/10.1103/PhysRevA.64.034101[Crossref]
- [10] C. Lin, T. Hsiung, M. Huang, Europhys. Lett. 83, 30002 (2008) http://dx.doi.org/10.1209/0295-5075/83/30002[Crossref]
- [11] M. V. Berry, N. J. Balazs, Am. J. Phys. 47, 264 (1979) http://dx.doi.org/10.1119/1.11855[Crossref]
- [12] J. N. Watson, A treatise on the theory of Bessel Functions, (Cambridge University Press, London 1966)
- [13] T. Haimo, C. Market, J. Math. Anal. Appl. 168, 89 (1992) http://dx.doi.org/10.1016/0022-247X(92)90191-F[Crossref]
- [14] G. Dattoli, B. Germano, P. E. Ricci, Appl. Math. Comput. 154, 219 (2004) http://dx.doi.org/10.1016/S0096-3003(03)00705-7[Crossref]
- [15] J. Lekner, Eur. J. Phys. 30, L43 (2009) http://dx.doi.org/10.1088/0143-0807/30/3/L04[Crossref]
- [16] G. Dattoli, K. Zhukovsky, arXiv:math-ph/1010.1678v1
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-011-0057-9