Displaying similar documents to “Dual series equations involving generalized Laguerre polynomials.”

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

Hans Weber (2007)

Open Mathematics

Similarity:

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...

Connections between Romanovski and other polynomials

Hans Weber (2007)

Open Mathematics

Similarity:

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.

Pseudo Laguerre and pseudo Hermite polynomials

Giuseppe Dattoli (2001)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

We start from pseudo hyperbolic and trigonometric functions to introduce pseudo Laguerre and Hermite polynomials. We discuss the link with families of Bessel functions and analyze all the associated problems from a unifying point of view, employing operational tools.