could any one give me a hint for this one? please not the whole solution Let f be a non constant rat

Blericker74 2022-07-16 Answered
could any one give me a hint for this one? please not the whole solution Let f be a non constant rational function and z 1 , , z n be its poles in C ¯ . we have to show that f can be written as f = f 1 + , f p where each f j is a rational function.
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Answers (1)

Keegan Barry
Answered 2022-07-17 Author has 18 answers
Under Robert Israel's interpretation, you can do induction on the number of poles. Expand f in Laurent series in { z : 0 < | z z n | < r } for sufficiently small r. The series has finitely many negative powers; puts them into f n . Apply the inductive hypotheses to f f n and conclude.
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