  We study the interpolation group whose elements are suitable pairs of formal
power series. This group has a faithful representation into infinite lower
triangular matrices and carries thus a natural structure as a Lie group. The
matrix exponential between its Lie algebra and its matrix representation gives
rise to a function with interesting properties extending the usual exponential
function to two variables (which are formal power series) We finish with an
application to enumerative combinatorics and the description of an algebra
which generalizes the interpolation group.
