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1: 1.13 Differential Equations
§1.13(i) Existence of Solutions
A domain in the complex plane is simply-connected if it has no “holes”; more precisely, if its complement in the extended plane { } is connected. … where z D , a simply-connected domain, and f ( z ) , g ( z ) are analytic in D , has an infinite number of analytic solutions in D . …
1.13.6 A w 1 ( z ) + B w 2 ( z ) = 0 , z D ,
2: 3.3 Interpolation
If f is analytic in a simply-connected domain D 1.13(i)), then for z D , … If f is analytic in a simply-connected domain D , then for z D , …