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Machinato
  • Member for 8 years, 7 months
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34 votes
6 answers
2k views

Conjectured value of $\int_{0}^{\infty}\left(\frac{x-1}{\ln^2 x}-\frac{1}{\ln x}\right)\frac{\mathrm{d}x}{x^2+1}$

14 votes
3 answers
2k views

Closed form for $\sum_{n=1}^{\infty}\frac{1}{\sinh^2\!\pi n}$ conjectured

8 votes
1 answer
321 views

Closed form for $\sum_{n=1}^{\infty}\frac{(-1)^n}{\sqrt{n^2+a^2}}$

7 votes
3 answers
226 views

General formula for $\int^1_0 x^\alpha \log(1-x)\operatorname{Li}_2 (x)\, \mathrm dx$

6 votes
2 answers
176 views

Integrate $\int_{a}^1 \frac{\left(1-t^2\right) \tanh^{-1}t }{t^6} \ln \left(\frac{t+\sqrt{-1+t^2/a^2}}{t-\sqrt{-1+t^2/a^2}}\right) dt$

6 votes
1 answer
147 views

When you can look through a forest?

4 votes
1 answer
269 views

Evaluate $\int^1_0 x^a (1-x)^b \operatorname{Li}_2 (x)\, \mathrm dx$

3 votes
1 answer
68 views

Elliptic definite integral $\int_0^1 x \left(\left(7+x^2\right) E\left(x\right) - 4 \left(1-x^2\right) K(x)\right)^2 \mathrm{d}x$

3 votes
1 answer
21 views

Rational vertices after affine transformations of polyhedra

3 votes
1 answer
199 views

Infinite sum of a product of associated Legendre polynomias

3 votes
2 answers
460 views

Inverse Laplace transform of $K_0 \left(r \sqrt{s^2-1}\right)$

3 votes
1 answer
118 views

Elliptic integral equality

3 votes
2 answers
1k views

Infinite product of sinc function

2 votes
1 answer
61 views

Evaluating double integral $\int_0^\infty\int_{-1}^1 r^{n-1} e^{-\alpha^2(r^2 - r x)} (1-x^2)^{\frac{n-3}{2}} \, \mathrm{d}x\, \mathrm{d}r$

2 votes
1 answer
60 views

Discrepancy in matrix determinant identity

2 votes
1 answer
59 views

Solving a functional equation $ g(x) = \frac{1}{1-x} g\left(\frac{ax}{1-x}\right) $

2 votes
1 answer
111 views

Asymptotic expansion of a coefficients given functional equation of the generating function

2 votes
0 answers
207 views

Solution of biharmonic differential equation on rectangular region with specific boundary conditions

1 vote
0 answers
47 views

Expected power of a determinant of a random matrix

1 vote
2 answers
235 views

Changing order of limit and complex derivative

1 vote
1 answer
39 views

Equation with matrix minors

1 vote
1 answer
84 views

Why can be Beta function formula used on divergent integrals as well?

1 vote
1 answer
57 views

A matrix equation equivalence

1 vote
1 answer
104 views

Solution of an integral equation

1 vote
1 answer
123 views

Closed form for $\sum_{n=0}^{\infty}\frac{x^n}{(n-a)^2+b^2}$

1 vote
1 answer
502 views

The Postman Problem

1 vote
0 answers
115 views

Green kernel for Dirichlet problem of Stokes flow PDE's $\nabla p = \Delta\vec{v}, \nabla\cdot\vec{v}=0$ on a sphere

0 votes
0 answers
37 views

Guess four functions given their boundary derivatives

0 votes
1 answer
99 views

Proving $|\operatorname{Aut}(E/F)|\leq\left[E:F\right]$ for $E$ splitting field [duplicate]

0 votes
0 answers
60 views

Closed form of $\sum _{k=0}^n \frac{(n-k)!}{(k+1) (2 n -k +2)!}$