Open AccessON CUBATURE RULES ASSOCIATED TO WEYL GROUP ORBIT FUNCTIONS
Author(s) -
Lenka Háková,
Jiří Hrivnák,
Lenka Motlochová
Publication year - 2016
Publication title -
acta polytechnica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.207
H-Index - 15
eISSN - 1805-2363
pISSN - 1210-2709
DOI - 10.14311/ap.2016.56.0202
Subject(s) - mathematics , weyl group , orbit (dynamics) , simple (philosophy) , special functions , group (periodic table) , pure mathematics , generality , elementary function , lie algebra , algebra over a field , diagram , mathematical analysis , physics , quantum mechanics , philosophy , statistics , epistemology , engineering , aerospace engineering , psychology , psychotherapist
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 C 2 .