Difference between revisions of "Analytic continuation"

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(Created page with "In complex analysis we may consider extending the domain of a given function <math> f(z) </math> which is Dictionary:analytic Function|analy...")
 
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by finding another function <math> g(z) </math> analytic in a region <math> {\mathcal R}_2 </math>, if a region <math> {\mathcal R}_3 </math> exists such
 
by finding another function <math> g(z) </math> analytic in a region <math> {\mathcal R}_2 </math>, if a region <math> {\mathcal R}_3 </math> exists such
 
that <math> {\mathcal R}_3 = {\mathcal R} \cap {\mathcal R}_2 </math>. We say that <math> g(z) </math> is ''the analytic continuation'' of <math> f(z) </math>
 
that <math> {\mathcal R}_3 = {\mathcal R} \cap {\mathcal R}_2 </math>. We say that <math> g(z) </math> is ''the analytic continuation'' of <math> f(z) </math>
into <math> {\mathcal R}_2 </math>
+
into <math> {\mathcal R}_2 </math>.

Revision as of 11:27, 11 April 2016

In complex analysis we may consider extending the domain of a given function which is analytic in a region by finding another function analytic in a region , if a region exists such that . We say that is the analytic continuation of into .