I depared myself with this problem
And studyins it I have made the assumption that if A is equal to a finite value then the expression is equivalent to
. studying this new function in terms of a , the function is increasing up to a=e , and after that point is decreasing .
How do I prove that there for all numbers greater than e , there arenآ´t any x that solves this equation ? How to study properly the convergence or divergence of this function?
Asking again ,how do I conclude that the function is diverging for X superior to e ?
For xx superior to ee, can you say that the function is increasing?
– ذ°رپر‚ذ¾ذ½ ذ²ر–ذ»ذ»ذ° ذ¾ذ»ذ¾ر„ ذ¼رچذ»ذ»ذ±رچر€ذ³
2 days ago
I wasn’t entirely clear in my question . after the first assumption I begin to study the fuction f(a)=a^(1/a) , this function is increasing up to a= e ,And it has a maximum on that point (a,x) (e ,e^(1/e)).So ,if i prove that
so if i prove that the function x rise to x …..infinite times ,is increasiing after that point I prove taht is divergent after that point?
Euler showed that
See this for discussion and references:
I found this with
a Google search for
“euler exponential tower”.