Zonai harmonic functions from two dimensional analogs of jacobi polynomials

Abstract

The Class I orthogonal polynomials in the complex variables z and are reviewed [7]. These polynomials are two dimensional analogs of the Jacobi polynomials and are orthogonal on the unit disk with respect to the weight function The polynomials are then shown to be eigenfunctions of a certain partial differential operator. Using these polynomials class of zonal, harmonic, homogeneous polynomials is defined in . In the case that n-2, applications to electrostatic potentials are given.

AMS(MOS)Classification Number:

• 33A65