List questions from closed-form

Published on 27 Mar 2026 - 23:48

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Improper Integral $\int\limits_0^{\frac12}(2x - 1)^6\log^2(2\sin\pi x)\,dx$

Published on 17 Dec 2013 - 9:54

585

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Infinite Series $\sum\limits_{n=1}^\infty\frac{\zeta(3n)}{2^{3n}}$

Published on 06 Apr 2026 - 20:35

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Infinite Series $\sum\limits_{n=1}^\infty\frac{x^{3n}}{(3n-1)!}$

Published on 17 Dec 2013 - 15:26

2.6k

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Integral $\int_{0}^{3} \frac{e^{-x^2}}{\sqrt{1-x^2}} \,dx$

Published on 21 Dec 2013 - 8:54

372

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Closed form for $\sum\limits_{k=1}^{\infty}\zeta(4k-2)-\zeta(4k)$

Published on 06 Apr 2026 - 20:34

56

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Closed form for a special recursion?

Published on 05 Apr 2026 - 16:59

127

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Evaluate $\sum_{n=1}^{\infty} \frac{\ln n}{(n+1)!}$

Published on 30 Dec 2013 - 16:13

81

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Generating function of $ \lim_{x\rightarrow 0} \frac{1}{n!} \frac{\partial^n}{\partial x^n} [(1+ax)^n f(x)] $

Published on 31 Dec 2013 - 17:41

607

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I flip M coins, my opponent flips N coins. Who has more heads wins. Is there a closed form for probability?

Published on 02 Apr 2026 - 3:50

188

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Determinant of parametric function and $0!1!2!...n!$

Published on 07 Apr 2026 - 7:07

309

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Closed form for $\sum_{k=1}^{\infty} \zeta(2k)-\zeta(2k+1)$

Published on 06 Apr 2026 - 22:16

262

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Integrating a complicated function

Published on 01 Apr 2026 - 1:30

222

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Closed form for a trigonometric partial sum

Published on 29 Mar 2026 - 11:20

596

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Evaluating $\int_0^1 \frac{\text{Li}_2 \left(-\frac{1}{1-z}\right)-\text{Li}_2 \left(-\frac{1}{1+z}\right)}{z}dz$

Published on 21 Jan 2014 - 8:40

List Question

Infinite Series $\sum\limits_{n=1}^\infty\frac{H_{2n+1}}{n^2}$

Improper Integral $\int\limits_0^{\frac12}(2x - 1)^6\log^2(2\sin\pi x)\,dx$

Infinite Series $\sum\limits_{n=1}^\infty\frac{\zeta(3n)}{2^{3n}}$

Infinite Series $\sum\limits_{n=1}^\infty\frac{x^{3n}}{(3n-1)!}$

Integral $\int_{0}^{3} \frac{e^{-x^2}}{\sqrt{1-x^2}} \,dx$

Closed form for $\sum\limits_{k=1}^{\infty}\zeta(4k-2)-\zeta(4k)$

Closed form for a special recursion?

Evaluate $\sum_{n=1}^{\infty} \frac{\ln n}{(n+1)!}$

Generating function of $ \lim_{x\rightarrow 0} \frac{1}{n!} \frac{\partial^n}{\partial x^n} [(1+ax)^n f(x)] $

I flip M coins, my opponent flips N coins. Who has more heads wins. Is there a closed form for probability?

Determinant of parametric function and $0!1!2!...n!$

Closed form for $\sum_{k=1}^{\infty} \zeta(2k)-\zeta(2k+1)$

Integrating a complicated function

Closed form for a trigonometric partial sum

Evaluating $\int_0^1 \frac{\text{Li}_2 \left(-\frac{1}{1-z}\right)-\text{Li}_2 \left(-\frac{1}{1+z}\right)}{z}dz$

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