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2007 | 5 | 3 | 253-284
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Romanovski polynomials in selected physics problems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties. We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula.
Wydawca
Czasopismo
Rocznik
Tom
5
Numer
3
Strony
253-284
Opis fizyczny
Daty
wydano
2007-09-01
online
2007-09-01
Twórcy
  • Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, 78290, San Luis Potosí, México
autor
  • Instituto de Física, Universidad Autónoma de San Luis Potosí, 78290, San Luis Potosí, México
  • Instituto de Física, Universidad Autónoma de San Luis Potosí, 78290, San Luis Potosí, México
Bibliografia
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  • [6] D.E. Alvarez-Castillo and M. Kirchbach: “Exact spectrum and wave functions of the hyperbolic Scarf potential in terms of finite Romanovski polynomials”, E-Print Archive: quant-ph/0603122.
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  • [21] W. Greiner and B. Müller: Quantum Mechanics: Symmetries, 2nd rev. ed., Springer, Berlin-Heidelberg, 2004; G.F. Torres del Castillo and J.L. Calvario Acócal: “On the Dynamical Symmetry of the Quantum Kepler Problem”, Rev. Mex. Fis., Vol. 44(4), (1998), pp. 344–352.
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  • [29] W. Koepf and M. Masjed-Jamei: “A Generic Polynomial Solution for the Differential Equation of Hypergeometric Type and Six Sequences of Orthogonal Polynomials”, Integral Transforms and Special Functions, Vol. 17, (2006), pp. 559–576; M. Masjed-Jamei: “Classical Orthogonal Polynomials with Weight Function ((ax + b)2 + (cx + d)2)−p exp(q) arctan \(\tfrac{{ax + b}}{{cx + d}}x \in ( - \infty , + \infty )\) and Generalization of T and F Distributions”, Integral Transforms and Special Functions, Vol. 15, (2002), pp. 137–153. http://dx.doi.org/10.1080/10652460600725234[Crossref]
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-007-0018-5
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