Open AccessON CONNECTING WEYL-ORBIT FUNCTIONS TO JACOBI POLYNOMIALS AND MULTIVARIATE (ANTI)SYMMETRIC TRIGONOMETRIC FUNCTIONS
Author(s) -
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.2016.56.0283
Subject(s) - mathematics , connection (principal bundle) , chebyshev polynomials , orbit (dynamics) , trigonometric functions , orthogonal polynomials , pure mathematics , combinatorics , mathematical analysis , geometry , engineering , aerospace engineering
The aim of this paper is to make an explicit link between the Weyl-orbit functions and the corresponding polynomials, on the one hand, and to several other families of special functions and orthogonal polynomials on the other. The cornerstone is the connection that is made between the one-variable orbit functions of A 1 and the four kinds of Chebyshev polynomials. It is shown that there exists a similar connection for the two-variable orbit functions of A 2 and a specific version of two variable Jacobi polynomials. The connection with recently studied G 2 -polynomials is established. Formulas for connection between the four types of orbit functions of B n or C n and the (anti)symmetric multivariate cosine and sine functions are explicitly derived.