Question

Simple Expression - Lambert W function

score 77 · Answer 1 · 2026-03-25 14:18:27

77

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Simple Expression - Lambert W function

Published on 25 Mar 2026 - 14:18

score 531 · Answer 2 · 2019-08-03 18:13:34

531

Views

A closed form for the sum $\frac{a}{b}+\frac{a\cdot(a+1)}{b\cdot(b+1)}+\frac{a\cdot(a+1)\cdot(a+2)}{b\cdot(b+1)\cdot(b+2)}+\cdots$

Published on 03 Aug 2019 - 18:13

score 83 · Answer 3 · 2019-08-04 21:30:11

83

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Series $\sum _{n=0}^{\infty } \frac{1}{(2 n+1)^m (2 n+3)^m (2 n+5)^m }$ and zeta function

Published on 04 Aug 2019 - 21:30

score 65 · Answer 4 · 2019-08-05 09:57:23

65

Views

Differential on Lie group $SO(3)$

Published on 05 Aug 2019 - 9:57

score 102 · Answer 5 · 2019-08-06 16:14:35

102

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How many cells are in a skew diagonal of a square matrix

Published on 06 Aug 2019 - 16:14

score 221 · Answer 6 · 2026-03-25 09:47:13

221

Views

Curious closed forms of the $q$-Gamma function.

Published on 25 Mar 2026 - 9:47

score 170 · Answer 7 · 2026-03-26 06:22:17

170

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Prove that $\int_{-1}^{1}\frac{\log(1+x)}{1+x^2}dx = \frac{\pi}{4}\log(2)-\sum_{n=0}^{\infty}\frac{(-1)^n}{(2n+1)^2}$

Published on 26 Mar 2026 - 6:22

score 342 · Answer 8 · 2019-08-14 07:08:15

342

Views

Is there a closed form for $\int_a^b\frac{{\rm arccosh}x}{\sqrt{(x-a)(b-x)}}$?

Published on 14 Aug 2019 - 7:08

score 66 · Answer 9 · 2019-08-16 00:01:51

66

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What is $\int_0^{p} e^{\frac{-(\ln(x)-\mu)^2}{2 \sigma^2}}\, dx$

Published on 16 Aug 2019 - 0:01

score 216 · Answer 10 · 2019-08-17 20:46:57

216

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Show the integral identity $\int_0^1 \frac{\ln(1-x) (\ln(1+x))^2}{x} dx = -\frac{\pi^4}{240}$

Published on 17 Aug 2019 - 20:46

score 2.2k · Answer 11 · 2019-08-22 08:31:04

2.2k

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Proving $\int_{\sqrt{\frac{3}{5}}}^1 \frac{\arctan (x)}{\sqrt{2 x^2-1} \left(3 x^2-1\right)} \, dx=\frac{3 \pi ^2}{160}$

Published on 22 Aug 2019 - 8:31

score 173 · Answer 12 · 2026-03-25 04:39:19

173

Views

Closed form for the series: $\sum_{n=1}^{\infty}x^{n^2}$

Published on 25 Mar 2026 - 4:39

score 98 · Answer 13 · 2019-08-23 22:06:15

98

Views

Evaluating this sum. Is there a closed form?

Published on 23 Aug 2019 - 22:06

score 92 · Answer 14 · 2019-08-24 12:45:53

92

Views

Controllability Gramian via integration by parts

Published on 24 Aug 2019 - 12:45

score 388 · Answer 15 · 2019-08-26 19:15:06

388

Views

Closed form of orthogonal projection onto a hyper-plane in $\mathbb{R}^{n\times n}$ constrained in the P.S.D. cone

Published on 26 Aug 2019 - 19:15

List Question

Simple Expression - Lambert W function

A closed form for the sum $\frac{a}{b}+\frac{a\cdot(a+1)}{b\cdot(b+1)}+\frac{a\cdot(a+1)\cdot(a+2)}{b\cdot(b+1)\cdot(b+2)}+\cdots$

Series $\sum _{n=0}^{\infty } \frac{1}{(2 n+1)^m (2 n+3)^m (2 n+5)^m }$ and zeta function

Differential on Lie group $SO(3)$

How many cells are in a skew diagonal of a square matrix

Curious closed forms of the $q$-Gamma function.

Prove that $\int_{-1}^{1}\frac{\log(1+x)}{1+x^2}dx = \frac{\pi}{4}\log(2)-\sum_{n=0}^{\infty}\frac{(-1)^n}{(2n+1)^2}$

Is there a closed form for $\int_a^b\frac{{\rm arccosh}x}{\sqrt{(x-a)(b-x)}}$?

What is $\int_0^{p} e^{\frac{-(\ln(x)-\mu)^2}{2 \sigma^2}}\, dx$

Show the integral identity $\int_0^1 \frac{\ln(1-x) (\ln(1+x))^2}{x} dx = -\frac{\pi^4}{240}$

Proving $\int_{\sqrt{\frac{3}{5}}}^1 \frac{\arctan (x)}{\sqrt{2 x^2-1} \left(3 x^2-1\right)} \, dx=\frac{3 \pi ^2}{160}$

Closed form for the series: $\sum_{n=1}^{\infty}x^{n^2}$

Evaluating this sum. Is there a closed form?

Controllability Gramian via integration by parts

Closed form of orthogonal projection onto a hyper-plane in $\mathbb{R}^{n\times n}$ constrained in the P.S.D. cone

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