Connections between Romanovski and other polynomials

Details Connections between Romanovski and other polynomials Connections between Romanovski and other polynomials

2007-06-21

arxiv.org/abs/0706.3153v1

Mathematics

Classical Analysis and ODEs

17 pages, no figures, to appear in Central European J. Math. (2007)

Scientific paper

A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schr\"odinger 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.

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