Pseudo Laguerre and pseudo Hermite polynomials

Giuseppe Dattoli

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2001)

  • Volume: 12, Issue: 2, page 75-84
  • ISSN: 1120-6330

Abstract

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We start from pseudo hyperbolic and trigonometric functions to introduce pseudo Laguerre and Hermite polynomials. We discuss the link with families of Bessel functions and analyze all the associated problems from a unifying point of view, employing operational tools.

How to cite

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Dattoli, Giuseppe. "Pseudo Laguerre and pseudo Hermite polynomials." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 12.2 (2001): 75-84. <http://eudml.org/doc/252293>.

@article{Dattoli2001,
abstract = {We start from pseudo hyperbolic and trigonometric functions to introduce pseudo Laguerre and Hermite polynomials. We discuss the link with families of Bessel functions and analyze all the associated problems from a unifying point of view, employing operational tools.},
author = {Dattoli, Giuseppe},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Hermite polynomials; Laguerre polynomials; Operator; operator},
language = {eng},
month = {6},
number = {2},
pages = {75-84},
publisher = {Accademia Nazionale dei Lincei},
title = {Pseudo Laguerre and pseudo Hermite polynomials},
url = {http://eudml.org/doc/252293},
volume = {12},
year = {2001},
}

TY - JOUR
AU - Dattoli, Giuseppe
TI - Pseudo Laguerre and pseudo Hermite polynomials
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2001/6//
PB - Accademia Nazionale dei Lincei
VL - 12
IS - 2
SP - 75
EP - 84
AB - We start from pseudo hyperbolic and trigonometric functions to introduce pseudo Laguerre and Hermite polynomials. We discuss the link with families of Bessel functions and analyze all the associated problems from a unifying point of view, employing operational tools.
LA - eng
KW - Hermite polynomials; Laguerre polynomials; Operator; operator
UR - http://eudml.org/doc/252293
ER -

References

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  1. Ricci, P.E., Le funzioni pseudo iperboliche e pseudo trigonometriche. Pubblicazione dell’Istituto di Matematica Applicata, n. 192, 1978. Zbl0423.33008
  2. Dattoli, G. - Torre, A., Theory and applications of generalized Bessel functions. Aracne, Roma1996. Zbl1018.33003
  3. Dattoli, G. - Torre, A., Operational methods and two-variable Laguerre polynomials. Atti Accademia di Torino, 132, 1998, 1-7. Zbl1098.33501MR1734597
  4. Andrews, L.C., Special functions for engineers and applied mathematicians. MacMillan, New York1985. Zbl0920.33001MR779819
  5. Dattoli, G. - Lorenzutta, S. - Mancho, A.M. - Torre, A., Generalized polynomials and associated operational identities. J. Comp. Appl. Math., 108, 1999, 209-218. Zbl0949.33005MR1705737DOI10.1016/S0377-0427(99)00111-9
  6. Nieto, M.N. - Truax, D.R., Arbitrary order Hermite generating functions for obtaining higher-order coherent and squeezed states. Phys. Lett., A208, 1995, 8-16. Zbl1020.33500
  7. Dattoli, G. - Torre, A., Generalized generating functions. Nuovo Cimento, 113B, 1998, 271-273. MR1624648
  8. Konhauser, J.D.E., Biorthogonal polynomials suggested by the Laguerre polynomials. Pacific J. Math., 21, 1967, 303-314. Zbl0156.07401MR214825
  9. Ben Cheikh, Y., Decomposition of some complex functions with respect to the cyclic group of order n . Appl. Math. Infor., 4, 2000. Zbl1060.30503MR1820846
  10. Ben Cheikh, Y., Decomposition of Laguerre polynomials with respect to the cyclic group of order n . J. Comp. Appl. Math., 99, 1998, 55-66. Zbl0930.33003MR1662683DOI10.1016/S0377-0427(98)00145-9
  11. Dattoli, G. - Srivastava, H.M. - Cesarano, C., On a new family of Laguerre polynomials. Atti Accademia di Torino, submitted. 
  12. Srivastava, H.M. - Singhal, J.P., A class of polynomials defined by generalized Rodriguez formula. Ann. Math. Pur. Appl., 90, 1971, 75-85. Zbl0197.34102MR308482
  13. W.B. Colson - G. Pellegrini – A. Renieri (eds.), Laser handbook. Vol. 6, North Holland, Amsterdam1990. 

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