  Orbit functions of a simple Lie group/Lie algebra L consist of exponential
functions summed up over the Weyl group of L. They are labeled by the highest
weights of irreducible finite dimensional representations of L. They are of
three types: C-, S- and E-functions. Orbit functions of the Lie algebras An, or
equivalently, of the Lie group SU(n+1), are considered.
  First, orbit functions in two different bases - one orthonormal, the other
given by the simple roots of SU(n) - are written using the isomorphism of the
permutation group of n elements and the Weyl group of SU(n).
  Secondly, it is demonstrated that there is a one-to-one correspondence
between classical Chebyshev polynomials of the first and second kind, and C-
and $S$-functions of the simple Lie group SU(2).
  It is then shown that the well-known orbit functions of SU(n) are
straightforward generalizations of Chebyshev polynomials to n-1 variables.
Properties of the orbit functions provide a wealth of properties of the
polynomials.
  Finally, multivariate exponential functions are considered, and their
connection with orbit functions of SU(n) is established.
