Displaying similar documents to “Pseudo Laguerre and pseudo Hermite polynomials”

Connections between Romanovski and other polynomials

Hans Weber (2007)

Open Mathematics

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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

Hans Weber (2007)

Open Mathematics

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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...