bo198214 Wrote:I only see a two times iterated exponential on page 3745. Do you mean that with tetration???
Oops. Somehow it looked very promising even though it contains just:
\( e^x/{e^{e^x}} \)
I hoped to see \( (e^x)^{(e^{-x})} \)
But since Poisson distribution is :
\( x* e^{-x} = x/e^x \)
There could be such pattern for (nested) critical processes:
\( \ln(\ln(x))-> \ln(x)/x-> x/e^x-> e^x/{e^{e^x}}-> e^{e^x}/e^{e^{e^x}}-> \)
Also, \( e^x \) is just a special value for \( x^x=x[4]2 \)
Still, appearance of iterated exp indicates a new kind of process, and probably the by nesting it one finally arrives at tetration. Not yet though...
What should be done to make Area of \( (e^x)^{(e^{-x})} \)=1?
Ivars