10/02/2009, 02:55 AM

Hi.

I heard of a function called "exponential factorial" that works like this:

...

As one can see it is similar to tetration in that it involves a power tower, but it is not defined by iteration but by a different type of recurrence, similar to the factorial. Could there be a way to derive a smooth/analytic extension for this like there is with the factorial and gamma function and like how extensions have been proposed for tetration?

I heard of a function called "exponential factorial" that works like this:

...

As one can see it is similar to tetration in that it involves a power tower, but it is not defined by iteration but by a different type of recurrence, similar to the factorial. Could there be a way to derive a smooth/analytic extension for this like there is with the factorial and gamma function and like how extensions have been proposed for tetration?