Romanovski polynomials in selected physics problems

• Authors: Alvaro Raposo , Hans Weber , David Alvarez-Castillo , Mariana Kirchbach
• Languages of publication: EN

Abstracts

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.

Keywords

EN

Romanovski polynomials; Scarf potential; Rosen-Morse potential and random matrices; orthogonality; 02.30.Gp; 02.30.Hq; 02.30.Jr; 03.65.Ge

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2007
• Volume: 5
• Issue: 3
• Pages: 253-284

Dates

published

1 - 9 - 2007

online

1 - 9 - 2007

Contributors

author

Alvaro Raposo

• Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, 78290, San Luis Potosí, México

author

Hans Weber

• Department of Physics, University of Virginia, Charlottesville, VA, 22904, USA

author

David Alvarez-Castillo

• Instituto de Física, Universidad Autónoma de San Luis Potosí, 78290, San Luis Potosí, México

author

Mariana Kirchbach

• Instituto de Física, Universidad Autónoma de San Luis Potosí, 78290, San Luis Potosí, México

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Identifiers

DOI

10.2478/s11534-007-0018-5