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Complex Analysis:

Complex Analysis: Find all functions f which are meromorphic in a neighborhood of {|z| <= 1} and such that |f(z)| = 1 for |z| = 1, f has a double pole at z = 1/2, a triple zero at z = -1/3, and no other zeros or poles in {|z| < 1 }

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2 f has pole of order 2 at point z =
Hence function can be written as
f (z ) = g (z )
(z − 12
) .(z
2 1
+ 3 )3 and pole of order 3 at point z = − 1 ,
3 , for some analytic function g (z ) (1)...

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