analyticity of a function
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is there any function can be used to check if a function is analytic or not?
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Accepted Answer
John D'Errico
on 2 Jun 2015
Edited: John D'Errico
on 2 Jun 2015
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 Comments
Sean de Wolski
on 2 Jun 2015
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
on 29 Sep 2016
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?
More Answers (3)
Roger Stafford
on 2 Jun 2015
Edited: Walter Roberson
on 2 Jun 2015
A complex-valued function of a complex variable is defined as analytic if it satisfies the Cauchy-Riemann equations. See:
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Paul Bower
on 16 Nov 2023
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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