Question

Challenging integral: $\int_0^Z\frac{\alpha^{(1-x^2)}}{1-x^2} dx$

score 413 · Answer 1 · 2015-08-07 09:03:03

413

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Challenging integral: $\int_0^Z\frac{\alpha^{(1-x^2)}}{1-x^2} dx$

Published on 07 Aug 2015 - 9:03

score 311 · Answer 2 · 2026-03-28 11:35:20

311

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Proving $~\prod~\frac{\cosh\left(n^2+n+\frac12\right)+i\sinh\left(n+\frac12\right)}{\cosh\left(n^2+n+\frac12\right)-i\sinh\left(n+\frac12\right)}~=~i$

Published on 28 Mar 2026 - 11:35

score 261 · Answer 3 · 2015-08-09 06:37:14

261

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closed form is exact in euclidean space

Published on 09 Aug 2015 - 6:37

score 138 · Answer 4 · 2015-08-09 18:45:55

138

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A nifty series involving $\cosh(x)$

Published on 09 Aug 2015 - 18:45

score 230 · Answer 5 · 2026-04-01 18:29:04

230

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Closed form for $(2^1-1)(2^2-1)...(2^k-1)$?

Published on 01 Apr 2026 - 18:29

score 97 · Answer 6 · 2015-08-12 12:13:27

97

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Infinite Series $\sum_{m=1}^{\infty} \frac{(-1)^{m-1}}{m^m}$

Published on 12 Aug 2015 - 12:13

score 572 · Answer 7 · 2015-08-12 16:02:58

572

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Evaluating $\sum_{n \geq 1}\ln \!\left(1+\frac1{2n}\right) \!\ln\!\left(1+\frac1{2n+1}\right)$

Published on 12 Aug 2015 - 16:02

score 302 · Answer 8 · 2015-08-12 18:29:43

302

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How to prove that a sequence with recurrence relation has no closed form expression?

Published on 12 Aug 2015 - 18:29

score 212 · Answer 9 · 2026-03-26 04:31:11

212

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Transcendental equation $2 x n\cot (2x)= x^2 - n^2$

Published on 26 Mar 2026 - 4:31

score 164 · Answer 10 · 2015-08-14 14:11:36

164

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Finding the $n^{th}$ derivative of $\frac{x^n}{(1+x)}$

Published on 14 Aug 2015 - 14:11

score 287 · Answer 11 · 2015-08-14 15:26:17

287

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Does this functional equation have a non-trivial closed form solution?

Published on 14 Aug 2015 - 15:26

score 431 · Answer 12 · 2015-08-15 13:43:05

431

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Integral $\int_0^1 \ln(x)^n \operatorname{Ei}(x) \, dx$

Published on 15 Aug 2015 - 13:43

score 122 · Answer 13 · 2015-08-16 00:26:01

122

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$\sum_{n=1}^\infty \frac{1}{(n^2-1)!} - \sum_{n=1}^\infty \frac{1}{(7n+1)!}$ is almost $1+1/6$

Published on 16 Aug 2015 - 0:26

score 609 · Answer 14 · 2015-08-17 14:35:31

609

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Closed-form of the hypergeometric function ${_4F_3}\left(\begin{array}c1,1,\tfrac54,\tfrac74\\\tfrac32,2,2\end{array}\middle|\,-t\right)$

Published on 17 Aug 2015 - 14:35

score 262 · Answer 15 · 2026-03-29 07:40:26

262

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Is there a formulaic way to go from $\sum_{k=1}^{n} \frac{1}{k}$ back to $n$?

Published on 29 Mar 2026 - 7:40

List Question

Challenging integral: $\int_0^Z\frac{\alpha^{(1-x^2)}}{1-x^2} dx$

Proving $~\prod~\frac{\cosh\left(n^2+n+\frac12\right)+i\sinh\left(n+\frac12\right)}{\cosh\left(n^2+n+\frac12\right)-i\sinh\left(n+\frac12\right)}~=~i$

closed form is exact in euclidean space

A nifty series involving $\cosh(x)$

Closed form for $(2^1-1)(2^2-1)...(2^k-1)$?

Infinite Series $\sum_{m=1}^{\infty} \frac{(-1)^{m-1}}{m^m}$

Evaluating $\sum_{n \geq 1}\ln \!\left(1+\frac1{2n}\right) \!\ln\!\left(1+\frac1{2n+1}\right)$

How to prove that a sequence with recurrence relation has no closed form expression?

Transcendental equation $2 x n\cot (2x)= x^2 - n^2$

Finding the $n^{th}$ derivative of $\frac{x^n}{(1+x)}$

Does this functional equation have a non-trivial closed form solution?

Integral $\int_0^1 \ln(x)^n \operatorname{Ei}(x) \, dx$

$\sum_{n=1}^\infty \frac{1}{(n^2-1)!} - \sum_{n=1}^\infty \frac{1}{(7n+1)!}$ is almost $1+1/6$

Closed-form of the hypergeometric function ${_4F_3}\left(\begin{array}c1,1,\tfrac54,\tfrac74\\\tfrac32,2,2\end{array}\middle|\,-t\right)$

Is there a formulaic way to go from $\sum_{k=1}^{n} \frac{1}{k}$ back to $n$?

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