 One can characterize the existence of antiderivatives via path integrals in the complex plane, much like the case of functions of a real variable.Perhaps not surprisingly, "g" has an antiderivative "f" if and only if, for every γ path from "a" to "b", the path integral

Equivalently,

for any closed path γ.However, this formal similarity notwithstanding, possessing a complex-antiderivative is a much more restrictive condition than its real counterpart.