针对你这个第八章一文，大家看看维基百科怎么说=
Suppose f is an analytic function defined on a non-empty open subset U of the complex plane C. If V is a larger open subset of C, containing U, and F is an analytic function defined on V such that
then F is called an analytic continuation of f. In other words, the restriction of F to U is the function f we started with.
Analytic continuations are unique in the following sense: if V is the connected domain of two analytic functions F 1 and F 2 such that U is contained in V and for all z in U
F 1 (z) = F 2 (z) = f(z),
then
F 1 = F 2 on all of V. This is because F 1 − F 2 is an analytic function which vanishes on the open, connected domain U of f and hence must vanish on its entire domain. This follows directly from the identity theorem for holomorphic functions.
|
楼主
