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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Analytic Continuation; The Gamma and Zeta Functions
verfasst von : Joseph Bak, Donald J. Newman
Erschienen in: Complex Analysis
Verlag: Springer New York
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Suppose we are given a function
f
which is analytic in a region
D
. We will say that
f
can be continued analytically to a region
D
1
that intersects
D
if there exists a function
g
, analytic in
D
1
and such that
g
=
f
throughout
$$ D_1 \cap D_2 $$
. By the Uniqueness Theorem (6.9) any such continuation of
f
is uniquely determined. (It is possible, however, to have two analytic continuations
g
1
and
g
2
of a function
f
to regions
D
1
and
D
2
respectively with
$$ g_1 \ne g_2 $$
throughout
$$ D_1 \cap D_2 $$
. See Exercise 1.)