analytic function

Noun

analytic function (plural analytic functions)

1. Any smooth (infinitely differentiable) function f, defined on an open set D⊆ℂ( textit or⊆ℝ), whose value in some neighbourhood of any given point x_0∈D is given by the Taylor series ∑ₙ₌₀ ᪲(f⁽ⁿ⁾(x_0))/(n!)(x-x_0)ⁿ.
   • There is a large and important literature concerned with the question of how to characterize precisely the boundary values of analytic functions. For example, when the analytic functions are of Hardy Class H#42; in a half plane, then their boundary values are attained in the L2 norm and, in fact...1966, E. J. Beltrami, M. R. Wohlers, Distributions and the Boundary Values of Analytic Functions, Academic Press, page vii
   • Thus we have limited ourselves by boundary value problems for analytic functions, and some related problems. The constructive ideas are always in our mind, so, the basic goal of this book is to be useful for experts in analytic function theory and for nonspecialists in it, and even for...2000, Vladimir V. Mityushev, Sergei V. Rogosin, Constructive Methods for Linear and Nonlinear Boundary Value Problems for Analytic Functions: Theory and Applications, Chapman & Hall / CRC, page v
2. window function