analyticity of a function

Question

abdo desoki 2015-6-2

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https://ww2.mathworks.cn/matlabcentral/answers/222141-analyticity-of-a-function

评论： Torsten 2024-5-13

采纳的回答： John D'Errico

is there any function can be used to check if a function is analytic or not?

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Walter Roberson 2015-6-2

What form is the function in? Symbolic form?

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Answer 1

John D'Errico 2015-6-2

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编辑：John D'Errico 2015-6-2

Short answer, no.

Long answer, nnnnnooooooooooooo.

No function defined in terms of floating point arithmetic is even truly continuous. So you cannot come to any such conclusion about that function given only a black box that evaluates the function. There may be arbitrarily many nasty points in such a function, that possibly will never be found.

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Sean de Wolski 2015-6-2

在 MATLAB Online 中打开

Well if you're given a symbolic function, you could determine that it is analytic, so sometimes, yes:

syms x
isanalytic(cos(x))

Yes!

Derek 2016-9-29

There doesn't seem to be a function for "isanalytic( )". Is that a custom function you've built? Has it been renamed in a newer version? Or were you saying that it could be done in theory if you had such a function?

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Answer 2

Roger Stafford 2015-6-2

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编辑：Walter Roberson 2015-6-2

A complex-valued function of a complex variable is defined as analytic if it satisfies the Cauchy-Riemann equations. See:

http://en.wikipedia.org/wiki/Cauchy–Riemann_equations

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Paul Bower 2023-11-16

It's also interesting to note that analytic functions solve Laplace's equation. As a result they're sometimes called harmonic functions. Polynomial functions and functions with a convergent Taylor series are the most common analytic functions.

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