08/22/2009, 05:50 PM
(This post was last modified: 08/22/2009, 11:57 PM by Base-Acid Tetration.)

Uh Oh I saw a problem with the f-logarithm terminology. What if it can mean a function/operator being plugged into the exp's Taylor series (powers meaning iteration)? Someone might call THAT a functional exponential, in analog to the matrix exponential...

consider this example (just an example, don't say it's circular because i use exp's taylor series) this statement of analyticity of a function:

Iff the following statement holds true for all

then the function is analytic in

Can you call such a usage an operator exponential?

Annotation: if you're confused about my example:

(x-x0) is scalar multiplication by x-x0, and d/dx is the differentiation operator ...

so

Apply that to f, and you get:

"Plug in" x_0 to this resulting function: .

consider this example (just an example, don't say it's circular because i use exp's taylor series) this statement of analyticity of a function:

Iff the following statement holds true for all

then the function is analytic in

Can you call such a usage an operator exponential?

Annotation: if you're confused about my example:

(x-x0) is scalar multiplication by x-x0, and d/dx is the differentiation operator ...

so

Apply that to f, and you get:

"Plug in" x_0 to this resulting function: .