On 1 Feb, 09:05, James Dow Allen <jdallen2...@[EMAIL PROTECTED]
> wrote:
> e+e+e+e+...+e (N times) is e*N
> =A0 =A0 and can be defined for non-integer N
> e*e*e*e*...*e (N times) is e^N
> =A0 =A0 and can be defined for non-integer N
> What is e^e^e^...^e (N times) ?
> =A0 =A0 =A0Can it be defined for non-integer N?
It depends on whether you think a^b^c is
(a) (a^b)^c or (b) a^(b^c)
In case (a) e^e^e^...^e (N times) is e^(e^(N-1)) which is easily
extended to non-integer N
In case (b) - more usual since it is more interesting - the you are
looking at "tetration". It can be extended to non-integer N in
several different ways. See
http://en.wikipedia.org/wiki/Tetration#Extensio=
n_to_real_heights
