Recent content by Matt100

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    Graduate Integrals of the function f(z) = e^(1/z) (complex analysis)

    How do you integrate f(z) = e^(1/z) in the multiply connected domain {Rez>0}∖{2} It seems like integrals of this function are path independent in this domain since integrals of e^(1/z) exist everywhere in the domain {Rez>0}∖{2}. Is that correct?
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    Graduate Path dependence (Complex Analysis)

    Are the integrals of the function f(z) = (1/(z-2) + (1/(z+1) + e^(1/z) path independent in the following domain: {Rez>0}∖{2} The domain is not simply connected I know that path independence has 3 equivalent forms that are 1) Integrals are independent if for every 2 points and 2 contours...
  3. M

    Graduate Is f(z) = e^(z^2) for all z in C?

    Assume |f(z)| >= 1/3|e^(z^2)| for all z in C and that f(0) = 1 and that f(z) is entire. Prove that f(z) = e^(z^2) for all z in C. How do you start for this.