Integral function of order alpha

[jostpuur]

What does it mean when a function is said to be an integral function of order \alpha? \alpha is some real constant. I encountered this terminology in the context of complex analytic functions.

 

[jostpuur]

I just realized that a complex function being integral very probably means that it is analytic function \mathbb{C}\to\mathbb{C}, and in particular not only an analytic function \mathbb{C}\backslash\{z_1,\ldots, z_n\}\to\mathbb{C}. I already knew a name for these functions in Finnish, but didn't realize immediately that this is how it gets translated into English.

I'm still wondering about what the order of an integral function means.

 

[Gib Z]

I think perhaps this is what you are looking for:

http://mathworld.wolfram.com/FunctionOrder.html

 

[jostpuur]

Thanks, that appears to be precisely what I was after. The text I was reading deals with similar expressions when talking about order.

Looking at the Mathworld, I noticed that I would have recognized the term "entire function", but did not know that "integral function" is synonymous with it.