Displaying similar documents to “A deformation of commutative polynomial algebras in even numbers of variables”

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.

Generalized Krawtchouk polynomials: New properties

Norris Sookoo (2000)

Archivum Mathematicum

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Orthogonality conditions and recurrence relations are presented for generalized Krawtchouk polynomials. Coefficients are evaluated for the expansion of an arbitrary polynomial in terms of these polynomials and certain special values for generalized Krawtchouk polynomials are obtained. Summations of some of these polynomials and of certain products are also considered.