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Connections between Romanovski and other polynomials

100%

Weber H.

Open Mathematics

2007

tom 5

nr 3

581-595

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.

Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula

100%

Weber H.

Open Mathematics

2007

tom 5

nr 2

415-427

Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas. Applications to the classical polynomials are given.

Ograniczanie wyników

2 Open Mathematics

2 Weber H.

2 2007

Wyniki wyszukiwania

Connections between Romanovski and other polynomials

Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula