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Results tagged with closed-form-expressions
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user 12481
For questions that specifically ask for determining a closed form of equations, integrals etc.
1
vote
Is there a closed form of $\int_0^\frac12\dfrac{\text{arcsinh}^nx}{x^m}dx$?
Conjecture:
$$ I(3,3)=-2\, \left( {\it arcsinh} \left( 1/2 \right) \right) ^{3}-3/2\,
\left( {\it arcsinh} \left( 1/2 \right) \right) ^{2}\sqrt {5}+{
\frac {3}{20}}\,{\pi }^{2}$$
This holds to at …
- 25.4k
5
votes
Accepted
On the search for an explicit form of a particular integral
High precision numerical computations suggest:
$$c_1=73/5760 $$
$$c_2=3625/580608$$
$$c_3=5233001/1393459200$$
- 25.4k
2
votes
Does this equation has a closed-form solution for $t$? ($(1-p)\sum_{i=0}^{n}t^i = p\sum_{i=0...
Too long for comment, here is partial answer for $n=5$ per R B's request.
According to Maple:
n:=5:q:=(1-p)*sum(t^i,i=0..n)-p*sum( (1-t)^i,i=0 .. n):so:=solve(q,t):
so[1] and so[2] are complex and …
- 25.4k
6
votes
Accepted
sum of integral part of n/k
For questions like this searching for the first few terms
in OEIS might help 3, 5, 8, 10, 14, 16, 20, 23, 27, 29, 35, 37, 41
This is A006218.
There are a lot of references and bounds for the sum.
I …
- 25.4k
0
votes
looking for f(x) in f(x) = a.exp((x-f(x))/b)
According to Maple:
so:=solve( f(x)-exp(( x - f(x)) /B ),f(x));latex(so);
$$ f(x) =B{\it LambertW} \left( {{\rm e}^{{\frac {x}{B}}}}{B}^{-1} \right) $$
And for the title:
so:=solve( f(x)-A …
- 25.4k
7
votes
Is this combination of generalized polygamma and dilogarithm actually zero? $\Im\;\psi^{(-2)...
Edited Maple's $\psi$ disagrees with Wolfram Alpha and your integral,
so here are some conjectures with both:
According to Maple -- your equality fails with this definition of psi.
$$ 24 \Im{\psi^{( …
- 25.4k