Displaying similar documents to “An alternative definition of the Hermite polynomials related to the Dunkl Laplacian.”

Bi-axial Gegenbauer functions of the first and second kind

Alan Common (1996)

Banach Center Publications

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The classical orthogonal polynomials defined on intervals of the real line are related to many important branches of analysis and applied mathematics. Here a method is described to generalise this concept to polynomials defined on higher dimensional spaces using Bi-Axial Monogenic functions. The particular examples considered are Gegenbauer polynomials defined on the interval [-1,1] and the Gegenbauer functions of the second kind which are weighted Cauchy integral transforms over this...