# What is a smooth function?

1. Dec 2, 2009

### AxiomOfChoice

What is a "smooth" function?

If someone tells you to consider a "smooth" function on the complex plane, what does that mean, exactly? Does it mean that the partial derivatives of the real and imaginary parts exist and are continuous? Does it mean something else?

2. Dec 2, 2009

### quasar987

Re: What is a "smooth" function?

Usually, "let f be a smooth function" is an expression people use to be "let f be a function satisfying certain regularity conditions".

Ex: for a smooth enough map f:R^2-->R, we have equality of the mixed partial derivative. Here, smooth means C^2.

Sometimes also, people equate smooth with C^{infinity}.

I've never seen smooth to mean holomorphic though...