Every germ of a function admits a “maximal” form of this process defined on the étale space of the sheaf. There must exist at least one function on D for which this process fails on any Levi pseudoconvex set D. The result of performing this process along two paths is equal when the monodromy theorem is satisfied. (15[1])By the Fabry gap theorem, so long as its sequence of powers grows at most linearly, this process can be performed for a (*) complex power series beyond its disk of convergence. If it exists, the result of performing this process from a set U to a superset T is unique by the identity theorem for holomorphic functions. This process is needed to define values for the Riemann zeta function (10[1])for arguments with real part less than one. For 10 points, name this process that extends the domain of a complex function to a larger set. ■END■