Meaning of analytic continuation | Babel Free

Definitions

1. The practice of extending analytic functions.
   countable, uncountable
2. An extension of an analytic function which is itself analytic.
   countable, uncountable

Equivalents

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.”

“Since there are potentially many different ways to carry⟳ out this analytic continuation process⟳, there are questions of ambiguity and redundancy.”

“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.”

“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).”

“The set⟳ of all the analytic continuations of the given element f(z) is called the complete⟳ analytic function.”

CEFR level