Question

Closed form solution for linear dynamical systems

score 414 · Answer 1 · 2018-10-01 20:38:33

414

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Closed form solution for linear dynamical systems

Published on 01 Oct 2018 - 20:38

score 657 · Answer 2 · 2026-03-24 23:51:36

657

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Prove that $\int_0^1\frac{\operatorname{Li}_3(1-z)}{\sqrt{z(1-z)}}\mathrm dz=-\frac{\pi^3}{3}\log 2+\frac{4\pi}3\log^3 2+2\pi\zeta(3)$

Published on 24 Mar 2026 - 23:51

score 60 · Answer 3 · 2018-10-06 19:07:34

60

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Closed form for $0^n0!+1^n1!+\cdots+k^nk!$

Published on 06 Oct 2018 - 19:07

score 90 · Answer 4 · 2018-10-07 16:58:23

90

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Closed form from recurrence

Published on 07 Oct 2018 - 16:58

score 199 · Answer 5 · 2018-10-08 21:08:14

199

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Is it possible to solve $\cos(x) + 2e^{x} = 0$ analytically?

Published on 08 Oct 2018 - 21:08

score 104 · Answer 6 · 2018-10-09 19:39:40

104

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

Published on 09 Oct 2018 - 19:39

score 225 · Answer 7 · 2026-03-25 17:41:55

225

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$\lim\limits_{s\to0^+}\sum_n\frac{\cos\left(\pi\frac{n}{m}\right)}{n^s}$ & $\lim\limits_{s\to0^+}\sum_n\frac{\sin\left(\pi\frac{n}{m}\right)}{n^s}$

Published on 25 Mar 2026 - 17:41

score 80 · Answer 8 · 2018-10-10 03:37:45

80

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closed form formula question

Published on 10 Oct 2018 - 3:37

score 79 · Answer 9 · 2018-10-12 20:21:11

79

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Solving (or approximating a solution of) $c = (1+a)^x - (1-a)^x$

Published on 12 Oct 2018 - 20:21

score 122 · Answer 10 · 2018-10-14 21:12:46

122

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Closed-form expression for infinite series related to a Gaussian

Published on 14 Oct 2018 - 21:12

score 102 · Answer 11 · 2018-10-14 23:17:27

102

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How to find the closed form solution for the multivariate recurrence?

Published on 14 Oct 2018 - 23:17

score 65 · Answer 12 · 2026-03-24 22:08:35

65

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Special solution to $a+e^a\ln x = x+e^a\ln a = a+e^x\ln a$

Published on 24 Mar 2026 - 22:08

score 443 · Answer 13 · 2018-10-16 00:55:58

443

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Is there a closed form expression for the first zero of the first Bessel function?

Published on 16 Oct 2018 - 0:55

score 84 · Answer 14 · 2018-10-17 02:44:44

84

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Looking for closed-form solution of the following integral

Published on 17 Oct 2018 - 2:44

score 935 · Answer 15 · 2018-10-18 21:47:39

935

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Integral $\int_0^1 \frac{(x^2+1)\ln(1+x)}{x^4-x^2+1}dx$

Published on 18 Oct 2018 - 21:47

List Question

Closed form solution for linear dynamical systems

Prove that $\int_0^1\frac{\operatorname{Li}_3(1-z)}{\sqrt{z(1-z)}}\mathrm dz=-\frac{\pi^3}{3}\log 2+\frac{4\pi}3\log^3 2+2\pi\zeta(3)$

Closed form for $0^n0!+1^n1!+\cdots+k^nk!$

Closed form from recurrence

Is it possible to solve $\cos(x) + 2e^{x} = 0$ analytically?

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

$\lim\limits_{s\to0^+}\sum_n\frac{\cos\left(\pi\frac{n}{m}\right)}{n^s}$ & $\lim\limits_{s\to0^+}\sum_n\frac{\sin\left(\pi\frac{n}{m}\right)}{n^s}$

closed form formula question

Solving (or approximating a solution of) $c = (1+a)^x - (1-a)^x$

Closed-form expression for infinite series related to a Gaussian

How to find the closed form solution for the multivariate recurrence?

Special solution to $a+e^a\ln x = x+e^a\ln a = a+e^x\ln a$

Is there a closed form expression for the first zero of the first Bessel function?

Looking for closed-form solution of the following integral

Integral $\int_0^1 \frac{(x^2+1)\ln(1+x)}{x^4-x^2+1}dx$

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