New families of $E$-functions are described in the context of the compactView original: http://arxiv.org/abs/1202.5031
simple Lie groups O(5) and G(2). These functions of two real variables
generalize the common exponential functions and for each group, only one family
is currently found in the literature. All the families are fully characterized,
their most important properties are described, namely their continuous and
discrete orthogonalities and decompositions of their products.