2
votes
Accepted
Is it possible to express $\int_{0+\epsilon}^{1-\epsilon}\left(\sqrt{1-x^2}^{\sqrt{1-x^2}^{\cdots}}\right) dx$ in elementary functions?
I think this is
$$
-\int_{0+\epsilon}^{1-\epsilon}
{\frac {2\;{\rm W} \left(-\frac12\,\ln \left( 1-{x
}^{2} \right) \right)}{\ln \left( 1-{x}^{2} \right) }}\,{\rm d}x
$$
not elementary.
- 41.1k
1
vote
Time ordered integral involving beta function:
I presume with "the case $n=2$" you mean the integral
$$\beta_2(n,m,p,q)=\int _0^1\int _0^t(1-t)^m t^n s^p (1-s)^qdsdt=\frac{m!(n+p+1)!}{(p+1) (m+n+p+2)!}\,\, _3F_2(p+1,n+p+2,-q;p+2,m+n+p+3;1)$$
which ...
- 188k
Only top scored, non community-wiki answers of a minimum length are eligible