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2011 | 9 | 6 | 1381-1386
Tytuł artykułu

The Airy transform and associated polynomials

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
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.
Wydawca

Czasopismo
Rocznik
Tom
9
Numer
6
Strony
1381-1386
Opis fizyczny
Daty
wydano
2011-12-01
online
2011-10-15
Twórcy
  • 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
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