"If a holomorphic function is defined on a closed disk and on the boundary of disk, function is known then by using Cauchy integral formula, we can determine the function in the interior of disk. In the same way, if we have a soap bubble formed on a closed wire and shape of wire (...
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Holomorphic FunctionA synonym for analytic function, regular function, differentiable function, complex differentiable function, and holomorphic map (Krantz 1999, p. 16). The word derives from the Greek (holos), meaning "whole," and (morphe), meaning "form" or "appearance." Many mathematicians ...
The Cauchy integral formula in Clifford analysis allows us to associate a holomorphic function $${\tilde{f}}:L_n\rightarrow {\mathbb C}$$ on the Lie ball $
function and the values of the corresponding stem function, showing that a slice-regular function vanishes if and only if the corresponding stem function takes values in a given complex analytic subset of{{\mathbb {C}}}^4. This allows us to recover in this setting a number of properties of...
This chapter is in the book Complex Analysis 2 Holomorphicfunctions2.1 ThederivativeoftherealvaluedcomplexfunctionsDefinition2.1.1.Thefunctionf:[a,b]→ℂissaidtobedifferentiableatthepointt0∈[a,b],ifthereexistthelimitlimt→t0f(t)−f(t0)t−t0=f(t0)∈ℂ.Usingthefactthatf(t)−f(t0...
[生肉]Complex Analysis: (XI) Power Series Are Holomorphic Proof 14播放 [生肉]Complex Analysis: (XII)Exp Cos and Sin as Power Series 7播放 [生肉]Complex Analysis: (IX)Power Series 4播放 [生肉]Complex Analysis: (X) Uniform Convergence 3播放 [生肉]Complex Analysis: (IV)Holomorphic and Entire...
Holomorphic almost periodic functions in tube domains and their amoebas Computational Methods and Function Theory, 1 (2) (2001), pp. 403-415 Google Scholar [10] S. Favorov, N. Parfyonova Meromorphic almost periodic functions Matematychni Studii, 13 (2) (2000), pp. 190-198 Google Scholar...
The most important superoscillatory function, that appears in connection with weak values in quantum mechanics, is Fn(x, a) = cos x n + i a sin x n n = n C j (n, a)ei(1−2 j/n)x , x ∈ R, j =0 (1) where a > 1 and the coefficients C j (n, a) are given by...
Using the variables t=1/x and w=y/x, the function 1/ζ has the following expansion in a neighborhood of the point p=[1:0:0]: 1ζ=t(1+tα(t,w)), where α(t,w) is a power series in t, w converging near p. Proof We recall the expression of the Hénon map in the va...