Analytic Continuation

The process of extending a holomorphic function from an initial domain to a larger domain by uniquely patching overlapping power-series or local representations, continuing along paths until an obstruction is reached.

The process of extending the domain of a holomorphic (analytic) function beyond its original region by defining it on larger domains so that on overlaps the extension agrees with the original function; extensions are unique when connectedness and analyticity conditions hold.

The process of extending a holomorphic (complex-analytic) function from its original domain to a larger connected region by using the unique continuation properties of analytic functions, typically by continuing power series or values along paths.