analyticity of a function
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is there any function can be used to check if a function is analytic or not?
1 个评论
Walter Roberson
2015-6-2
What form is the function in? Symbolic form?
采纳的回答
John D'Errico
2015-6-2
编辑：John D'Errico
2015-6-2
3 个投票
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.
2 个评论
Sean de Wolski
2015-6-2
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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Roger Stafford
2015-6-2
编辑：Walter Roberson
2015-6-2
1 个投票
A complex-valued function of a complex variable is defined as analytic if it satisfies the Cauchy-Riemann equations. See:
1 个评论
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.
Mandadi
2024-5-13
0 个投票
Test whetere f(z) =(x^2-y^2)+i(2*x*y) is analytic or not
2 个评论
Walter Roberson
2024-5-13
I don't think this solves the original question.
Torsten
2024-5-13
It equals f(z) = z^2. So yes: it's analytic.
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