# Thread: Complex analysis - functions that involve branch points/cuts

1. ## 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:

$f(z) = z^{\frac{1}{2}} ,
f(z) = \ln(z) ,
f(z) = \arctan(z)$

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

2. 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.