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  3. what is the residue of f(z) =1/(z-1) ^3 at its pol

What is the residue of f(z) =1/(z-1) ^3 at its pole? give details Explaination

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What is the residue of f(z) =1/(z-1) ^3 at its pole? give details Explaination

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3.7 Ratings (671 Votes)

The function f(z)=1/(z?1)3 has an isolated singularity at z=1 That isolated singularity is a pole of order 3

 

The Laurent series expansion of f(z) in any deleted neighbourhood of z=1 is ?n=??an(z?1)n

 

where a?3=1 and an=0 forn??3. In particular, Resz=1f(z)=a?1=0

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