monomocoso
New member
- Joined
- Jan 25, 2012
- Messages
- 31
I am having trouble understanding how to calculate residues.
I have the function
\(\displaystyle f(z)=\frac {z^a}{1+z^2}\) and am supposed to find
\(\displaystyle \int^\infty_0 f(z)\,dz\) using the keyhole contour. So I found singularities at +i and - i and am trying to find the residues there using
\(\displaystyle \lim_{z\to+i}\frac{{z^a}{(z-i)}}{1+z^2}\) and \(\displaystyle \lim_{z\to-i}\frac{{z^a}{(z+i)}}{1+z^2} \)
Is ths the right way to find residues? What are these limits?
I have the function
\(\displaystyle f(z)=\frac {z^a}{1+z^2}\) and am supposed to find
\(\displaystyle \int^\infty_0 f(z)\,dz\) using the keyhole contour. So I found singularities at +i and - i and am trying to find the residues there using
\(\displaystyle \lim_{z\to+i}\frac{{z^a}{(z-i)}}{1+z^2}\) and \(\displaystyle \lim_{z\to-i}\frac{{z^a}{(z+i)}}{1+z^2} \)
Is ths the right way to find residues? What are these limits?
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