Analytic Continuation Along A Curve
The definition of analytic continuation along a curve is a bit technical, but the basic idea is that one starts with an analytic function defined around a point, and one extends that function along a curve via analytic functions defined on small overlapping disks covering that curve.
Formally, consider a curve (a continuous function) Let be an analytic function defined on an open disk centered at An analytic continuation of the pair along is a collection of pairs for such that
- and
- For each is an open disk centered at and is an analytic function
- For each there exists such that for all with one has that (which implies that and have a non-empty intersection) and the functions and coincide on the intersection
Read more about this topic: Monodromy Theorem
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