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Homework Statement
1) [tex]\frac{e^{z}-1}{z}[/tex]
Locate the isolated singularity of the function and tell what kind of singularity it is.
2) [tex]\frac{1}{1 - cos(z)}[/tex]
z_0 = 0
find the laurant series for the given function about the indicated point. Also, give the residue of the function at the point.
Homework Equations
The Attempt at a Solution
1) I thought that it first was a removable singularity. Because of only z in the denominator. But I don't get why the value at 0 is 1 ? I attempted to use g(z) = z, calculate with H(z)/(z - z_0) But that didn't help me in the understanding of the question. So my question really is how do you know what the value is at the 0. And how do you calculate the singularity with more rigour!
2) First thing I saw was [tex]\frac{1}{1 - z}[/tex] and that is [tex]e^{z}[/tex]
But then I thought that maybe you take the taylor expansion of cos z and [tex]e^{z}[/tex] and multiply them. But from there it went downhill
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