Question

Juantheron-like integral

score 758 · Answer 1 · 2016-06-09 04:19:04

758

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Juantheron-like integral

Published on 09 Jun 2016 - 4:19

score 1k · Answer 2 · 2026-04-06 11:37:26

1k

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Integral $\int_{-\infty}^\infty\frac{\Gamma(x)\,\sin(\pi x)}{\Gamma\left(x+a\right)}\,dx$

Published on 06 Apr 2026 - 11:37

score 164 · Answer 3 · 2016-06-10 12:00:35

164

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Integration of Laguerre polynomial $\int_{0}^{x}u^{p-1}(1-u)^{q-1}e^{-\theta u}L_n^{(m)}(\theta u)\mathrm du$

Published on 10 Jun 2016 - 12:00

score 853 · Answer 4 · 2026-03-29 05:50:07

853

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Does this integral $\int_0^\infty \frac{dx}{(1+e^x)(a+x)}$ have a closed form?

Published on 29 Mar 2026 - 5:50

score 269 · Answer 5 · 2026-03-28 23:59:51

269

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Has it been proven that there is no closed form for the hailstone numbers?

Published on 28 Mar 2026 - 23:59

score 80 · Answer 6 · 2016-06-10 19:54:12

80

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Does this probability statement have a closed form? (Extreme value distribution)

Published on 10 Jun 2016 - 19:54

score 1.3k · Answer 7 · 2026-03-26 20:38:02

1.3k

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Polynomials with degree $5$ solvable in elementary functions?

Published on 26 Mar 2026 - 20:38

score 496 · Answer 8 · 2026-04-01 03:45:38

496

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Closed form of infinite product $\prod\limits_{k=0}^\infty 2 \left(1-\frac{x^{1/2^{k+1}}}{1+x^{1/2^{k}}} \right)$

Published on 01 Apr 2026 - 3:45

score 643 · Answer 9 · 2026-03-30 03:02:12

643

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Evaluate $\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1+5\sqrt{1+...}}}}}$

Published on 30 Mar 2026 - 3:02

score 260 · Answer 10 · 2016-06-19 21:08:08

Calculate two sums: $\sum_{i=1}^{99}\frac{1}{\sqrt{i+1}+\sqrt{i}}$, $\sum_{i=1}^{9999}\frac{1}{(\sqrt{i}+\sqrt{i+1}) (\sqrt[4]{i}+\sqrt[4]{i+1})}$.

score 243 · Answer 11 · 2016-06-20 09:42:56

243

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Closed form for $\int_0^1 \frac{1}{u + \lambda} \ln \left(\frac{1 + u}{1 - u} \right) ~d u$

Published on 20 Jun 2016 - 9:42

score 81 · Answer 12 · 2026-03-28 20:04:23

81

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Does this sequence have a closed form representation?

Published on 28 Mar 2026 - 20:04

score 2.8k · Answer 13 · 2016-06-20 18:26:58

2.8k

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Average value of $f(x)=\int_x^1 \cos(t^2) \,dt$ on the interval $[0,1]$.

Published on 20 Jun 2016 - 18:26

score 671 · Answer 14 · 2026-04-05 23:46:10

671

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Seeking closed form for infinite sum $\sum \limits_{ n=1 }^{ \infty }{ \frac { { \left(n! \right) }^{ 2 } }{ { n }^{ 3 }(2n)! } }$

Published on 05 Apr 2026 - 23:46

score 202 · Answer 15 · 2016-06-22 16:20:38

202

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Proving $\sum\limits_{k=0}^n \sum\limits_{j=0}^{n-k} \frac{(k-1)^2}{k!} \frac{(-1)^j}{j!} =1$ without character theory

Published on 22 Jun 2016 - 16:20

List Question

Juantheron-like integral

Integral $\int_{-\infty}^\infty\frac{\Gamma(x)\,\sin(\pi x)}{\Gamma\left(x+a\right)}\,dx$

Integration of Laguerre polynomial $\int_{0}^{x}u^{p-1}(1-u)^{q-1}e^{-\theta u}L_n^{(m)}(\theta u)\mathrm du$

Does this integral $\int_0^\infty \frac{dx}{(1+e^x)(a+x)}$ have a closed form?

Has it been proven that there is no closed form for the hailstone numbers?

Does this probability statement have a closed form? (Extreme value distribution)

Polynomials with degree $5$ solvable in elementary functions?

Closed form of infinite product $\prod\limits_{k=0}^\infty 2 \left(1-\frac{x^{1/2^{k+1}}}{1+x^{1/2^{k}}} \right)$

Evaluate $\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1+5\sqrt{1+...}}}}}$

Calculate two sums: $\sum_{i=1}^{99}\frac{1}{\sqrt{i+1}+\sqrt{i}}$, $\sum_{i=1}^{9999}\frac{1}{(\sqrt{i}+\sqrt{i+1}) (\sqrt[4]{i}+\sqrt[4]{i+1})}$.

Closed form for $\int_0^1 \frac{1}{u + \lambda} \ln \left(\frac{1 + u}{1 - u} \right) ~d u$

Does this sequence have a closed form representation?

Average value of $f(x)=\int_x^1 \cos(t^2) \,dt$ on the interval $[0,1]$.

Seeking closed form for infinite sum $\sum \limits_{ n=1 }^{ \infty }{ \frac { { \left(n! \right) }^{ 2 } }{ { n }^{ 3 }(2n)! } }$

Proving $\sum\limits_{k=0}^n \sum\limits_{j=0}^{n-k} \frac{(k-1)^2}{k!} \frac{(-1)^j}{j!} =1$ without character theory

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