03/29/2009, 10:37 AM

04/09/2009, 10:35 AM

Ansus Wrote:

Since , we derive f(x).

Though I dont know where from you got this formula, if I assume that the formula is correct and slightly reformulate it:

for on the imaginary axis :

then it can also be used to iteratively compute the superexponential (base ) on the imaginary axis:

Any volunteer to implement this formula?

PS: This formula needs no assumption about the value of convergence of for , the only arbitrarity is the choosen branch of logarithm.

04/09/2009, 04:57 PM

bo198214 Wrote:

I just see that the formula is not yet usable for implementation, but if we substitute then we have the same range of the imaganiray axis left and right:

04/09/2009, 06:10 PM

Ansus Wrote:

Since , we derive f(x).

But now I doubt the formula is true.

Setting for example .

Then

But if I compute this numerially I get on the right side something close to 0.

While the left side is .

Where did you get this formula? Is it applicable only to certain functions?

04/24/2009, 05:29 PM

Ansus Wrote:Quote:I mean without references I can not conclude that myself.It is NĂ¶rlundâ€“Rice integral (http://en.wikipedia.org/wiki/N%C3%B6rlun...e_integral).

bo198214 Wrote:Is it applicable only to certain functions?

See Ansus, your formula is only applicable to (in the right halfplane) polynomially bounded functions , you can read it in your reference. So it is not applicable here, and I dont need to wonder why the formula doesnt work.