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Results tagged with closed-form-expressions
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user 51189
For questions that specifically ask for determining a closed form of equations, integrals etc.
-2
votes
1
answer
258
views
Is it possible to express $\int_{0+\epsilon}^{1-\epsilon}\left(\sqrt{1-x^2}^{\sqrt{1-x^2}^{\...
let $\epsilon >0$, I tried to evaluate $\int_{0+\epsilon}^{1-\epsilon}\left(\sqrt{1-x^2}^{\sqrt{1-x^2}^{\cdots}}\right) dx$ , using the fact $x= \cos t$ yield to have integrand using $\sin $ functio …
1
vote
1
answer
293
views
Closed form of :$\int_{-1}^1 x^{2k} (\operatorname{erf}(x))^k \,dx $ for $ k$ is even intege...
This question is related to my question here such that i want to find a closed form of $\int_{-1}^1 x^{2k} (\operatorname{erf}(x))^k \,dx $ , for $k$ is even integer because for odd integer is $0$ as …
16
votes
3
answers
3k
views
How do i solve this : $\displaystyle \ f'=e^{{f}^{-1}}$?
Let $f$ be a function such that :$f:\mathbb{R}\to \mathbb{R}$ and $f^{-1}$ is a compositional inverse of $f$. I would'd like to know how do I solve this class of differential equation : $$\displ …