Question

How to compute $\int^{\infty}_{0} t^{(\frac1n-1)}\cos t \,\mathrm{d}t$?

score 175 · Answer 1 · 2026-04-06 19:36:18

175

Views

How to compute $\int^{\infty}_{0} t^{(\frac1n-1)}\cos t \,\mathrm{d}t$?

Published on 06 Apr 2026 - 19:36

score 527 · Answer 2 · 2013-05-26 19:58:45

527

Views

Is there a simpler closed form for $\sum_{n=1}^\infty\frac{(2n-1)!!\ (2n+1)!!}{4^n\ (n+2)\ (n+2)!^2}$

Published on 26 May 2013 - 19:58

score 229 · Answer 3 · 2013-05-26 20:58:15

229

Views

Sylvester's sequence: is there an exact closed form?

Published on 26 May 2013 - 20:58

score 1.4k · Answer 4 · 2026-03-30 01:48:05

1.4k

Views

How to prove $\int_0^\infty J_\nu(x)^3dx\stackrel?=\frac{\Gamma(1/6)\ \Gamma(1/6+\nu/2)}{2^{5/3}\ 3^{1/2}\ \pi^{3/2}\ \Gamma(5/6+\nu/2)}$?

Published on 30 Mar 2026 - 1:48

score 927 · Answer 5 · 2026-03-30 01:52:04

927

Views

Is $K\left(\frac{\sqrt{2-\sqrt3}}2\right)\stackrel?=\frac{\Gamma\left(\frac16\right)\Gamma\left(\frac13\right)}{4\ \sqrt[4]3\ \sqrt\pi}$

Published on 30 Mar 2026 - 1:52

score 1k · Answer 6 · 2013-05-28 04:11:50

1k

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What is a closed form of $\int_0^1\ln(-\ln x)\ \text{li}\ x\ dx$

Published on 28 May 2013 - 4:11

score 115 · Answer 7 · 2013-05-28 23:27:26

115

Views

Estimate the scale of the power series with Poisson pdf-like terms

Published on 28 May 2013 - 23:27

score 1.2k · Answer 8 · 2026-03-29 20:51:35

1.2k

Views

How to calculate $\sum_{n=1}^\infty\frac{(-1)^n}n H_n^2$?

Published on 29 Mar 2026 - 20:51

score 5.7k · Answer 9 · 2026-04-06 19:33:11

5.7k

Views

Is it possible to simplify $\frac{\Gamma\left(\frac{1}{10}\right)}{\Gamma\left(\frac{2}{15}\right)\ \Gamma\left(\frac{7}{15}\right)}$?

Published on 06 Apr 2026 - 19:33

score 1.1k · Answer 10 · 2013-06-03 07:07:40

1.1k

Views

A Challenging Euler Sum $\sum\limits_{n=1}^\infty \frac{H_n}{\tbinom{2n}{n}}$

Published on 03 Jun 2013 - 7:07

score 724 · Answer 11 · 2026-04-02 11:15:14

724

Views

Closed form of $\sum\limits_{i=1}^n\left\lfloor\frac{n}{i}\right\rfloor^2$?

Published on 02 Apr 2026 - 11:15

score 288 · Answer 12 · 2013-06-08 04:23:48

288

Views

Limit of an integral related to the beta function: $\int_0^1 \frac{v^\beta\,dv}{1-z v}\log\frac{1-v z}{1-v}$.

Published on 08 Jun 2013 - 4:23

score 165 · Answer 13 · 2013-06-08 18:52:29

165

Views

Integral of two logs and a power: $\int_0^1 u^c \log(1-au)\log(1-bu)\,\mathrm du$

Published on 08 Jun 2013 - 18:52

score 832 · Answer 14 · 2013-06-09 13:44:23

832

Views

The value of the $\lim_{n\rightarrow \infty}\frac{1}{n}\sum_{k=1}^{n}\frac{\sqrt[k]{k!}}{k}$

Published on 09 Jun 2013 - 13:44

score 125 · Answer 15 · 2026-04-06 19:34:31

125

Views

Closed form of specific series

Published on 06 Apr 2026 - 19:34

List Question

How to compute $\int^{\infty}_{0} t^{(\frac1n-1)}\cos t \,\mathrm{d}t$?

Is there a simpler closed form for $\sum_{n=1}^\infty\frac{(2n-1)!!\ (2n+1)!!}{4^n\ (n+2)\ (n+2)!^2}$

Sylvester's sequence: is there an exact closed form?

How to prove $\int_0^\infty J_\nu(x)^3dx\stackrel?=\frac{\Gamma(1/6)\ \Gamma(1/6+\nu/2)}{2^{5/3}\ 3^{1/2}\ \pi^{3/2}\ \Gamma(5/6+\nu/2)}$?

Is $K\left(\frac{\sqrt{2-\sqrt3}}2\right)\stackrel?=\frac{\Gamma\left(\frac16\right)\Gamma\left(\frac13\right)}{4\ \sqrt[4]3\ \sqrt\pi}$

What is a closed form of $\int_0^1\ln(-\ln x)\ \text{li}\ x\ dx$

Estimate the scale of the power series with Poisson pdf-like terms

How to calculate $\sum_{n=1}^\infty\frac{(-1)^n}n H_n^2$?

Is it possible to simplify $\frac{\Gamma\left(\frac{1}{10}\right)}{\Gamma\left(\frac{2}{15}\right)\ \Gamma\left(\frac{7}{15}\right)}$?

A Challenging Euler Sum $\sum\limits_{n=1}^\infty \frac{H_n}{\tbinom{2n}{n}}$

Closed form of $\sum\limits_{i=1}^n\left\lfloor\frac{n}{i}\right\rfloor^2$?

Limit of an integral related to the beta function: $\int_0^1 \frac{v^\beta\,dv}{1-z v}\log\frac{1-v z}{1-v}$.

Integral of two logs and a power: $\int_0^1 u^c \log(1-au)\log(1-bu)\,\mathrm du$

The value of the $\lim_{n\rightarrow \infty}\frac{1}{n}\sum_{k=1}^{n}\frac{\sqrt[k]{k!}}{k}$

Closed form of specific series

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