Question

On the closed-form of the triple integral $\int_0^\infty\int_0^\infty\int_0^\infty\frac1{xyz\left(x+y+z+1/x+1/y+1/z\right)^2}\rm{dx\,dy\,dz}$

score 214 · Answer 1 · 2026-03-25 01:18:55

214

Views

On the closed-form of the triple integral $\int_0^\infty\int_0^\infty\int_0^\infty\frac1{xyz\left(x+y+z+1/x+1/y+1/z\right)^2}\rm{dx\,dy\,dz}$

Published on 25 Mar 2026 - 1:18

score 122 · Answer 2 · 2019-06-10 16:38:54

122

Views

Bound on $x$ for $x-\ln x\ge 1+\epsilon$

Published on 10 Jun 2019 - 16:38

score 66 · Answer 3 · 2026-03-26 17:47:48

66

Views

Solve and asymptotic expansion of $\sum_{a=1}^{H} \sum_{b=a+1}^{H} \left\lfloor{\frac{H}{a\, b}}\right\rfloor$

Published on 26 Mar 2026 - 17:47

score 61 · Answer 4 · 2019-06-11 01:48:01

61

Views

$n$th derivative of $\sqrt{\frac{(s_0+T)(s_0 + T + 2\sqrt{a})}{(s+T)(s+ T+2\sqrt{a})}}$

Published on 11 Jun 2019 - 1:48

score 313 · Answer 5 · 2019-06-11 16:18:32

313

Views

Summation closed form

Published on 11 Jun 2019 - 16:18

score 758 · Answer 6 · 2026-03-25 19:06:27

758

Views

How to evaluate $\int_{0}^{1}\frac{\arctan x}{x} \log{\left(\frac{ 1+ x}{\sqrt{1+x^2}}\right)}\mathrm dx$

Published on 25 Mar 2026 - 19:06

score 27 · Answer 7 · 2019-06-12 12:52:58

27

Views

Sequences with reocurring/doubled elements: closed expression

Published on 12 Jun 2019 - 12:52

score 170 · Answer 8 · 2019-06-12 17:01:32

170

Views

Solution of the integral $\int_1^\infty \frac{1}{x(e^{a x}-1)} dx$?

Published on 12 Jun 2019 - 17:01

score 910 · Answer 9 · 2026-03-25 11:16:06

910

Views

Compute $\int_0^\infty \frac{\operatorname{Li}_3(x)}{1+x^2}\ dx$

Published on 25 Mar 2026 - 11:16

score 258 · Answer 10 · 2019-06-14 11:23:17

258

Views

Integrals involving powers and beta (or hypergeometric) function

Published on 14 Jun 2019 - 11:23

score 45 · Answer 11 · 2019-06-16 08:23:15

45

Views

Expressing the coefficients of $(1-x)^{1/4}$ using factorials

Published on 16 Jun 2019 - 8:23

score 37 · Answer 12 · 2026-03-25 09:26:11

37

Views

Closed-form for $F(n) = \sum_{d|n} \omega_x(d) $

Published on 25 Mar 2026 - 9:26

score 177 · Answer 13 · 2019-06-27 17:57:12

177

Views

Find closed formula without using induction for $\sum_{k=0}^n k^3$

Published on 27 Jun 2019 - 17:57

score 192 · Answer 14 · 2019-06-28 21:28:27

192

Views

Prove $\sum_{n=1}^{\infty}\frac{\Gamma(n+\frac{1}{2})}{(2n+1)(2n+2)(n-1)!}=\frac{(4-π)\sqrt{\pi}}{4}$

Published on 28 Jun 2019 - 21:28

score 208 · Answer 15 · 2019-06-29 00:25:12

208

Views

Compute the following sum in closed form : $\sum_{n=1}^{\infty}\frac{n\binom{2n}{n}}{4^{n}(2n+1)(2n-1)(4n+1)}$

Published on 29 Jun 2019 - 0:25

List Question

On the closed-form of the triple integral $\int_0^\infty\int_0^\infty\int_0^\infty\frac1{xyz\left(x+y+z+1/x+1/y+1/z\right)^2}\rm{dx\,dy\,dz}$

Bound on $x$ for $x-\ln x\ge 1+\epsilon$

Solve and asymptotic expansion of $\sum_{a=1}^{H} \sum_{b=a+1}^{H} \left\lfloor{\frac{H}{a\, b}}\right\rfloor$

$n$th derivative of $\sqrt{\frac{(s_0+T)(s_0 + T + 2\sqrt{a})}{(s+T)(s+ T+2\sqrt{a})}}$

Summation closed form

How to evaluate $\int_{0}^{1}\frac{\arctan x}{x} \log{\left(\frac{ 1+ x}{\sqrt{1+x^2}}\right)}\mathrm dx$

Sequences with reocurring/doubled elements: closed expression

Solution of the integral $\int_1^\infty \frac{1}{x(e^{a x}-1)} dx$?

Compute $\int_0^\infty \frac{\operatorname{Li}_3(x)}{1+x^2}\ dx$

Integrals involving powers and beta (or hypergeometric) function

Expressing the coefficients of $(1-x)^{1/4}$ using factorials

Closed-form for $F(n) = \sum_{d|n} \omega_x(d) $

Find closed formula without using induction for $\sum_{k=0}^n k^3$

Prove $\sum_{n=1}^{\infty}\frac{\Gamma(n+\frac{1}{2})}{(2n+1)(2n+2)(n-1)!}=\frac{(4-π)\sqrt{\pi}}{4}$

Compute the following sum in closed form : $\sum_{n=1}^{\infty}\frac{n\binom{2n}{n}}{4^{n}(2n+1)(2n-1)(4n+1)}$

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