analyticity of a function

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

[Walter Roberson]

What form is the function in? Symbolic form?

Answer 1

[John D'Errico]

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.

[Sean de Wolski]

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]

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?

Answer 2

[Roger Stafford]

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

[Paul Bower]

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.

Answer 3

[Sharmi]

check whether f(z)=z^2 is analytic or not

[Torsten]

Yes, the function equals its Taylor series.