Romanovski polynomials in selected physics problems

Details Romanovski polynomials in selected physics problems Romanovski polynomials in selected physics problems

2007-06-26

arxiv.org/abs/0706.3897v1

Central European Journal of Physics, 5(3), 2007, pp. 253-284

Physics

Quantum Physics

RevTex, 38 pages, 2 figures, review

Scientific paper

10.2478/s11534-007-0018-5

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.

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