ON CUBATURE RULES ASSOCIATED TO WEYL GROUP ORBIT FUNCTIONS

Authors

  • Lenka Háková University of Chemistry and Technology, Prague
  • Jiří Hrivnák Czech Technical University in Prague
  • Lenka Motlochová Czech Technical University in Prague

DOI:

https://doi.org/10.14311/AP.2016.56.0202

Keywords:

Weyl group orbit functions, Jacobi polynomials, cubature formulas

Abstract

The aim of this article is to describe several cubature formulas related to the Weyl group orbit functions, i.e. to the special cases of the Jacobi polynomials associated to root systems. The diagram containing the relations among the special functions associated to the Weyl group orbit functions is presented and the link between the Weyl group orbit functions and the Jacobi polynomials is explicitly derived in full generality. The four cubature rules corresponding to these polynomials are summarized for all simple Lie algebras and their properties simultaneously tested on model functions. The Clenshaw-Curtis method is used to obtain additional formulas connected with the simple Lie algebra C2.

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Published

2016-06-30

How to Cite

Háková, L., Hrivnák, J., & Motlochová, L. (2016). ON CUBATURE RULES ASSOCIATED TO WEYL GROUP ORBIT FUNCTIONS. Acta Polytechnica, 56(3), 202–213. https://doi.org/10.14311/AP.2016.56.0202

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Articles