Connections between Romanovski and other polynomials
Open Mathematics (2007)
- Volume: 5, Issue: 3, page 581-595
- ISSN: 2391-5455
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topHans Weber. "Connections between Romanovski and other polynomials." Open Mathematics 5.3 (2007): 581-595. <http://eudml.org/doc/269170>.
@article{HansWeber2007,
abstract = {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.},
author = {Hans Weber},
journal = {Open Mathematics},
keywords = {Romanovski polynomials; complexified Jacobi polynomials; generating function; recursion relations; addition theorems; Rodrigues formula; orthogonal polynomials},
language = {eng},
number = {3},
pages = {581-595},
title = {Connections between Romanovski and other polynomials},
url = {http://eudml.org/doc/269170},
volume = {5},
year = {2007},
}
TY - JOUR
AU - Hans Weber
TI - Connections between Romanovski and other polynomials
JO - Open Mathematics
PY - 2007
VL - 5
IS - 3
SP - 581
EP - 595
AB - 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.
LA - eng
KW - Romanovski polynomials; complexified Jacobi polynomials; generating function; recursion relations; addition theorems; Rodrigues formula; orthogonal polynomials
UR - http://eudml.org/doc/269170
ER -
References
top- [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 Zbl17.0315.02
- [2] V. Romanovski: “Sur quelques classes nouvelles de polynomes orthogonaux”, C. R. Acad. Sci. Paris, Vol. 188, (1929), pp. 1023–1025. Zbl55.0915.03
- [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 Zbl1124.33011
- [7] G.B. Arfken and H.J. Weber: Mathematical Methods for Physicists, 6th ed., Elsevier-Academic Press, Amsterdam, 2005. Zbl1066.00001
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