# 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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