Question
In: Advanced Math
complex analysis
What is the residue of f(z) =1/(z-1) ^3 at its pole? give details Explaination
Solutions
Expert Solution
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
0
Arjoma Karan answered 2 years agoRelated Solutions
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