1. Let f(2) = where Vw = eLog w is the principal branch of the square root function. %3D (a) By considering branch cuts, explain why f is holomorphic on the region G = C\ {r €R:r<-1 or r2 1}. %3D (b) Which property of G ensures thatf has an antiderivative F on this set?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. Let f(2) = A where V = elog is the principal branch of
the square root function.
(a) By considering branch cuts, explain why f is holomorphic on the
region G = C\ {r €R:r<-1 orI 1}.
%3D
(b) Which property of G ensures thatf has an antiderivative F on
this set?
Transcribed Image Text:1. Let f(2) = A where V = elog is the principal branch of the square root function. (a) By considering branch cuts, explain why f is holomorphic on the region G = C\ {r €R:r<-1 orI 1}. %3D (b) Which property of G ensures thatf has an antiderivative F on this set?
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