fascinating average

[JmsNxn]

im currently fascinated by these sequences of " tetration averages ".

for integer a > 2

exp^[n]((ln^[n](a) + ln^[n](a+1))/2)

for n = 0 its AM for n = 1 its GM

the average , real part and im part , inf real , sup im , infinite sum over n etc

all seem intresting to me.

in particular for a = 17.

maybe there are simple answers.

using logarithmic semi-operators, for 0 <= q <= 1, your "fascinating average" is given as:

(n {q} n+1) {1+q} 1/2