Questions tagged [power-towers]

For questions pertaining to power towers: expressions like a^(b^(c^d))), which result from iterated exponentiation. The "hyperoperation" tag may be appropriate, too.

212 questions
Filter by
Sorted by
Tagged with
7 views

Using matrix algebra, can we show that the infinite power series [(1+x)/2]^N is equal to (1+x)/(1-x), ∀x∈[0,1[? [closed]

Can the answer be related to the assumption :[For positive symmetric physical power matrices, the sum of their eigenvalues is equal to the eigenvalue of their sum of power series]
24 views

• 357
188 views

Is it possible to express $\int_{0}^{1-\epsilon}\left(\sqrt{1-x^2}^{\sqrt{1-x^2}^{\cdots}}\right) dx$ in elementary functions?

let $\epsilon >0$, I tried to evaluate $\int_{0}^{1}\left(\sqrt{1-x^2}^{\sqrt{1-x^2}^{\cdots}}\right) dx$ , using the fact $x= \cos t$ yield to have integrand using $\sin$ function seems is not ...
• 6,572
1 vote
A version of the Shooting Room "paradox" involves selecting disjoint sets in the plane, first selecting a set of area $1$, then a set of area $r$, then of $r^2$, etc.--i.e. geometric growth--...