30A99-AnalyticContinuationByPowerSeries.tex

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\pmtitle{analytic continuation by power series}
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\begin{document}
Given a holomorphic function defined on some open set, one technique
for analytically continuing it to a larger set is by means of power
series.  One picks a point of the region and constructs the Taylor
series of the function about that point.  If it turns out that the
radius of convergence of the Taylor series is large enough that it
contains points which are not in the original domain, one can
extend the function to a larger domain obtrained by adding these points.
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