Tagged Questions
4
votes
1answer
149 views
Definite integral of tetration between $0$ and $1$
In my old writes I found next formula, where is ${_{}^2}x$ is tetration:
$$\int_0^1 {_{}^2}x \ dx = \sum\limits_{i=1}^\infty \frac {(-1)^{i+1}} {{_{}^2}i} \approx 0.783430511\ldots$$
And now I am ...
7
votes
3answers
456 views
How to calculate $f(x)$ in $f(f(x)) = e^x$?
How would I calculate the power series of $f(x)$ if $f(f(x)) = e^x$? Is there a faster-converging method than power series for fractional iteration/functional square roots?
