If f(z) has a branch point at z=0, what does 1/f(z) have at z=0?

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If f(z) has a pole of order n at z=0 then 1/f(z) has a zero of order n at z=0. Is there an equivalent for if f(z) has a branch point at z=0 instead? If f(z) has a branch point at z=0, what does 1/f(z) have at z=0?