Relation Between Polynomials Orthogonal with Respect to a Class of Gaussian Weight Functions

Abstract

Polynomials of a three-dimensional vector x, orthogonal with respect to a weight function ~exp( -tx2) and expressed in spherical polar coordinates, are called Burnett functions. The matrix relating the Burnett functions of x = IX(C- W) to those of c is constructed for the case where IX is a real nonsingular 3 x 3 matrix and W is a real vector. These matrices are infinite dimensional, block lower triangular representations of the group whose elements (IX, W) satisfy the composition law