Bi-axial Gegenbauer functions of the first and second kind
Volume 37 / 1996
Banach Center Publications 37 (1996), 181-187
DOI: 10.4064/-37-1-181-187
Abstract
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 interval of these polynomials. Related polynomials are defined which are orthogonal on the unit ball $
