Connections between Romanovski and other polynomials

• Autorzy: Hans Weber
• Języki publikacji: EN

Abstrakty

EN

A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schrödinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking the Rodrigues formula in an elementary and natural way. The generating function is summed in closed form from which recursion relations and addition theorems follow. Relations to some classical polynomials are also given.

Słowa kluczowe

EN

Romanovski polynomials; complexified Jacobi polynomials; generating function; recursion relations; addition theorems

Kategorie tematyczne

• 42C15: General harmonic expansions, frames
• 34B24: Sturm-Liouville theory
• 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2007
• Tom: 5
• Numer: 3
• Strony: 581-595

Daty

wydano

2007-09-01

online

2007-05-13

Twórcy

autor

Hans Weber

• University of Virginia

Bibliografia

• [1] E.J. Routh: “On some properties of certain solutions of a differential equation of second order”, Proc. London Math. Soc., Vol. 16, (1884), pp. 245–261. http://dx.doi.org/10.1112/plms/s1-16.1.245
• [2] V. Romanovski: “Sur quelques classes nouvelles de polynomes orthogonaux”, C. R. Acad. Sci. Paris, Vol. 188, (1929), pp. 1023–1025.
• [3] N. Cotfas: “Systems of orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics”, Cent. Eur. J. Phys., Vol. 2, (2004), pp. 456–466; “Shape invariant hypergeometric type operators with application to quantum mechanics”, Preprint: arXiv:math-ph/0603032. http://dx.doi.org/10.2478/BF02476425
• [4] C.B. Compean and M. Kirchbach: “The trigonometric Rosen-Morse potential in supersymmetric quantum mechanics and its exact solutions”, J. Phys. A-Math. Gen., Vol. 39, (2006), pp. 547–557. http://dx.doi.org/10.1088/0305-4470/39/3/007
• [5] A. Raposi, H.J. Weber, D. Alvarez-Castillo and M. Kirchbach: “Romanovski polynomials in selected physics problems”, Cent. Eur. J. Phys., to be published.
• [6] H.J. Weber: “Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula”, Cent. Eur. J. Math., Vol. 5, (2007), pp. 415–427. http://dx.doi.org/10.2478/s11533-007-0004-6
• [7] G.B. Arfken and H.J. Weber: Mathematical Methods for Physicists, 6th ed., Elsevier-Academic Press, Amsterdam, 2005.

Identyfikatory

DOI

10.2478/s11533-007-0014-4