  We develop and describe continuous and discrete transforms of class functions
on compact simple Lie group $G$ as their expansions into series of uncommon
special functions, called here $\E$-functions in recognition of the fact that
the functions generalize common exponential functions. The rank of $G$ is the
number of variables in the $\E$-functions. A uniform discretization of the
decomposition problem is described on lattices of any density and symmetry
admissible for the Lie group $G$.
