Then the extension formula given above is an analytic continuation to the whole complex plane.

The analytic continuation and functional equation then boil down to those of the Eisenstein series.

Note that the hyperfunction can be non-trivial, even if the components are analytic continuation of the same function.

It is used in quantum field theory to construct the analytic continuation of Wightman functions.

A number of issues were clarified, in particular that of analytic continuation.

The definition may be extended to all of the complex plane through analytic continuation.

Again, analytic continuation can be thwarted by function features that were not evident from the initial data.

The general theory of analytic continuation and its generalizations are known as sheaf theory.

This extension by transitivity is one definition of analytic continuation.

For other values of x and y the function F can be defined by analytic continuation.