  We present a new methodology for the characterization of the metric entropy
of infinite-dimensional ellipsoids with exponentially decaying semi-axes. This
procedure does not rely on the explicit construction of coverings or packings
and provides a unified framework for the derivation of the metric entropy of a
wide variety of analytic function classes, such as periodic functions analytic
on a strip, analytic functions bounded on a disk, and functions of exponential
type. In each of these cases, our results improve upon the best known results
in the literature.
