Question

$z_{n+1} = v z_n ^5 - (v-1) z_n $ with $ v = 3,06328648997749...$

score 84 · Answer 1 · 2026-03-25 22:05:36

84

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$z_{n+1} = v z_n ^5 - (v-1) z_n $ with $ v = 3,06328648997749...$

Published on 25 Mar 2026 - 22:05

score 103 · Answer 2 · 2019-09-20 20:00:25

103

Views

Closed form solution to $\int_0^{\infty} x(1+({\frac{x}{\lambda}})^{(-\alpha-1)}) dx$

Published on 20 Sep 2019 - 20:00

score 192 · Answer 3 · 2026-03-26 11:00:02

192

Views

Temperature of a categorical distribution with given logits and entropy

Published on 26 Mar 2026 - 11:00

score 162 · Answer 4 · 2026-03-26 06:34:55

162

Views

Proving $\sum\limits_{k=1}^{N-1}\left[\frac{\sin\left(\frac{\pi km}{N}\right)}{\sin\left(\frac{\pi k}{N}\right)}\right]^{2}=m(N-m)$

Published on 26 Mar 2026 - 6:34

score 341 · Answer 5 · 2019-09-21 07:46:15

341

Views

Evaluate $\sum _{n=1}^{\infty } \frac{\sin \left(x \sqrt{a^2+n^2}\right)}{\left(a^2+n^2\right)^{3/2}}$ and generalize it

Published on 21 Sep 2019 - 7:46

score 82 · Answer 6 · 2019-09-23 07:52:27

82

Views

Evaluate $\sum _{n=1}^{\infty } \frac{J_v(2 \pi n a)}{n^v}$

Published on 23 Sep 2019 - 7:52

score 282 · Answer 7 · 2026-03-25 13:34:20

282

Views

Infinite product $\Gamma(\tfrac14)=\mathrm{A}^3e^{-\mathrm{G}/\pi}2^{1/6}\sqrt{\pi}\prod_{k\ge1}\left(1-\frac1{2k}\right)^{(-1)^k k}$

Published on 25 Mar 2026 - 13:34

score 257 · Answer 8 · 2026-03-18 08:48:57

257

Views

$35.2850899... $ has a closed form ??

Published on 18 Mar 2026 - 8:48

score 68 · Answer 9 · 2026-03-26 04:35:03

68

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Does anyone see how I could shorten the following formula $\sum_{j=1}^n \left( \sum_{i \neq j}^n (x_i-x_j) x_i\right)^2$?

Published on 26 Mar 2026 - 4:35

score 118 · Answer 10 · 2019-09-27 19:29:45

118

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Compute in a closed form the following sum : $\sum_{n=1}^{+\infty}\frac{\Gamma^{4}(n+\frac{3}{4})}{(4n+3)^{2}\Gamma^{4}(n+1)}$

Published on 27 Sep 2019 - 19:29

score 236 · Answer 11 · 2019-09-28 18:40:19

236

Views

Calculate $\sum_{k=1}^{n} \frac{1}{1+k^2}$

Published on 28 Sep 2019 - 18:40

score 105 · Answer 12 · 2019-09-29 06:04:03

105

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Proving $\sum _{k=1}^{\infty } J_k(k z)^2=\frac{1}{2 \sqrt{1-z^2}}-\frac{1}{2}$

Published on 29 Sep 2019 - 6:04

score 91 · Answer 13 · 2019-09-29 15:38:32

91

Views

How to write $\sum_{n=0}^{N-1} \binom{2n}{n}x^{n+1}$ in closed form or short form?

Published on 29 Sep 2019 - 15:38

score 88 · Answer 14 · 2014-03-12 00:51:23

88

Views

Why we say this function have closed form while the other doesn't?

Published on 12 Mar 2014 - 0:51

score 411 · Answer 15 · 2014-03-12 12:38:51

411

Views

Closed Form for $\int_0^1 \frac{\log(x)}{\sqrt{1-x^2}\sqrt{x^2+2+2\sqrt{2}}}dx$

Published on 12 Mar 2014 - 12:38

List Question

$z_{n+1} = v z_n ^5 - (v-1) z_n $ with $ v = 3,06328648997749...$

Closed form solution to $\int_0^{\infty} x(1+({\frac{x}{\lambda}})^{(-\alpha-1)}) dx$

Temperature of a categorical distribution with given logits and entropy

Proving $\sum\limits_{k=1}^{N-1}\left[\frac{\sin\left(\frac{\pi km}{N}\right)}{\sin\left(\frac{\pi k}{N}\right)}\right]^{2}=m(N-m)$

Evaluate $\sum _{n=1}^{\infty } \frac{\sin \left(x \sqrt{a^2+n^2}\right)}{\left(a^2+n^2\right)^{3/2}}$ and generalize it

Evaluate $\sum _{n=1}^{\infty } \frac{J_v(2 \pi n a)}{n^v}$

Infinite product $\Gamma(\tfrac14)=\mathrm{A}^3e^{-\mathrm{G}/\pi}2^{1/6}\sqrt{\pi}\prod_{k\ge1}\left(1-\frac1{2k}\right)^{(-1)^k k}$

$35.2850899... $ has a closed form ??

Does anyone see how I could shorten the following formula $\sum_{j=1}^n \left( \sum_{i \neq j}^n (x_i-x_j) x_i\right)^2$?

Compute in a closed form the following sum : $\sum_{n=1}^{+\infty}\frac{\Gamma^{4}(n+\frac{3}{4})}{(4n+3)^{2}\Gamma^{4}(n+1)}$

Calculate $\sum_{k=1}^{n} \frac{1}{1+k^2}$

Proving $\sum _{k=1}^{\infty } J_k(k z)^2=\frac{1}{2 \sqrt{1-z^2}}-\frac{1}{2}$

How to write $\sum_{n=0}^{N-1} \binom{2n}{n}x^{n+1}$ in closed form or short form?

Why we say this function have closed form while the other doesn't?

Closed Form for $\int_0^1 \frac{\log(x)}{\sqrt{1-x^2}\sqrt{x^2+2+2\sqrt{2}}}dx$

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