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