04/01/2009, 05:49 PM

maybe this is the dumbest tetration question ever , but here goes.

i was thinking about a " tetration limit ".

as you all know , im particular intrested in half iterates of exponential functions.

we all know

lim n -> oo ( 1 + f(n) ) ^ n = e

if f(n) = 1/n

now this is the typical exponential limit.

but what is the typical half iterate exponential limit ?

lim n -> oo F [( 1 + f(n) ) ; n ] = Q = ???

where F stands for the half iterate exponential of base ( 1 + f(n) )

and f(n) and Q are the unknown function and unknown value.

regards

tommy1729

i was thinking about a " tetration limit ".

as you all know , im particular intrested in half iterates of exponential functions.

we all know

lim n -> oo ( 1 + f(n) ) ^ n = e

if f(n) = 1/n

now this is the typical exponential limit.

but what is the typical half iterate exponential limit ?

lim n -> oo F [( 1 + f(n) ) ; n ] = Q = ???

where F stands for the half iterate exponential of base ( 1 + f(n) )

and f(n) and Q are the unknown function and unknown value.

regards

tommy1729