Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options answers only not deleted user 12481

For questions that specifically ask for determining a closed form of equations, integrals etc.

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 …
joro's user avatar
  • 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 …
joro's user avatar
  • 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 …
joro's user avatar
  • 25.4k
5 votes
Accepted

On the search for an explicit form of a particular integral

High precision numerical computations suggest: $$c_1=73/5760 $$ $$c_2=3625/580608$$ $$c_3=5233001/1393459200$$
joro's user avatar
  • 25.4k
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 …
joro's user avatar
  • 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^{( …
joro's user avatar
  • 25.4k