ON CUBATURE RULES ASSOCIATED TO WEYL GROUP ORBIT FUNCTIONS

Acta Polytechnica

Lenka Háková¹  Lenka Motlochová²  Jiří Hrivnák² 

[1] University of Chemistry and Technology, Prague;Czech Technical University in Prague

关键词: Weyl group orbit functions;    Jacobi polynomials;    cubature formulas;   

DOI  :  

来源: Czech Technical University in Prague, Faculty of M

【 摘 要 】

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 algebraC2 .

【 授权许可】

Unknown