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Math Help - Complex analysis - functions that involve branch points/cuts

  1. #1
    Junior Member
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    Complex analysis - functions that involve branch points/cuts

    hey

    i was compiling a basic list of functions that need to be checked for branch points (as oppose to points of singularities)

    at the moment all i have are:

    f(z) = z^{\frac{1}{2}} , <br />
f(z) = \ln(z) , <br />
f(z) = \arctan(z)

    does anyone have anything to add this vague list?

    its not meant to be a formula sheet or anything, just a list of terms that if, cropping up in a contour integral type question, that i should associate with branch-point methods
    Last edited by CaptainBlack; October 9th 2009 at 11:26 PM.
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  2. #2
    Super Member
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    Any function which involves the complex logarithm either explicitly or implicitly is multivalued. So roots and inverse trigs are the standard ones. Seems to me, the inverse of any non-injective analytic function would be multivalued. For example, the inverse zeta and gamma functions are multivalued. The Lambert W function is multivalued.
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