Eight Kinds of Orthogonal Polynomials of the Weyl Group C₂ and the Tau Method

Abstract

The four kinds of the classical Chebyshev polynomials are generalized to eight kinds of two-variable polynomials of the Weyl group C₂. The admissible shift of the weight lattice and the four sign homomorphisms of C₂ generate eight types of the underlying hybrid character functions. The construction method of the resulting shifted four kinds of polynomials is detailed. The tau method for the approximation of solutions of differential equations using these two-variable polynomials is discussed.