Recent content by luke1001

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    Solve Cauchy Integral on Unit Circle: f'(z)/(z-zo) = f(z)/(z-zo)^2

    A. Homework Statement f is analytic inside and on a simple closed contour C and z0 isn't on C. Show: \int f'(z)dz/ (z- zo) = \int f(z)dz/ (z- zo)^2 The Attempt at a Solution \int f'(z)dz/ (z- zo) = 2\pii f'(zo)\int f(z)dz/ (z- zo)^2 = \int [f(z)dz/(z- zo)]/(z-zo) = 2\pii [f(zo)/(zo-zo)] (I...
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    Finding the Residue of f'/f at 0 with a Zero of Multiplicity k

    hmm, do you mean f is analytic at 0?
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    Finding the Residue of f'/f at 0 with a Zero of Multiplicity k

    Homework Statement Let f has a zero of multiplicity k at 0. Find the residue of f'/f at 0 The Attempt at a Solution I'm kind of get stuck on this one. I got only this far: Since f has a zero of multiplicity k at 0, then f(z) = (z^k)g(z) :( Thanks a lot for helping!