analytic continuation

Noun

analytic continuation (countable and uncountable, plural analytic continuations)

1. The practice of extending analytic functions.
   • The standard method of analytic continuation starts with a function f(z) defined by its power-series expansion (7.5-4) inside some circle |z-a|=r.1968, [McGraw-Hill], Granino A. Korn, Theresa M. Korn, Mathematical Handbook for Scientists and Engineers, 2000, Dover, Unabridged republication, page 206
   • Since there are potentially many different ways to carry out this analytic continuation process, there are questions of ambiguity and redundancy.2008, Steven G. Krantz, A Guide to Complex Variables, Mathematical Association of America, page 125
2. An extension of an analytic function which is itself analytic.
   • Using (2.6), (2.15)-(2.18) and (2.54) in the same way as in the cases considered earlier, we get that the series (0.14) determines the analytic continuation of the Green function of the second boundary value problem into the domain K_B∩|k|<β with the property (0.23).1975, S. Smith (translator), L. A. Muraveǐ Asymptotics for the Wave Equation, S. Smith (translator), Valentin P. Michaǐlov (editor), Boundary Value Problems for Differential Equations, Mathematical...
   • The set of all the analytic continuations of the given element f(z) is called the complete analytic function.1995, Valentin I. Ivanov, Michael K. Trubetskov, Handbook of Conformal Mapping with Computer-Aided Visualization, CRC Press, page 26