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

  • Tomasz CzyżyckiEmail author
  • Jiří Hrivnák
Conference paper
Part of the Trends in Mathematics book series (TM)

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.

Keywords

Weyl groups orthogonal polynomials tau method 

Mathematics Subject Classification (2010).

33C52 42A10 65N30 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of BiałystokBiałystokPoland
  2. 2.Czech Technical University in PraguePrague 1Czech Republic

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