analytic continuation

plural analytic continuations

1. countableuncountablemathematical analysisThe practice of extending analytic functions.

   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 more examples

   1968, [McGraw-Hill], Granino A. Korn, Theresa M. Korn, Mathematical Handbook for Scientists and Engineers, 2000, Dover, Unabridged republication, page 206, 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.

   Analytic continuation is a technique to extend the domain of a given analytic function. Analytic continuation often succeeds in defining further values of a function, for example, in a new region where an infinite series representation in terms of which it is initially defined becomes divergent.

   2014, M. Mursaleen, Applied Summability Methods, Springer, page 31

2. countableuncountablemathematical analysisAn extension of an analytic function which is itself analytic.

   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

   1 more example

   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 Association of America, page 107, 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).