Question

Is there a closed-form for $\sum_{n=0}^{\infty}\frac{n}{n^3+1}$?

score 318 · Answer 1 · 2026-03-26 21:26:22

318

Views

Is there a closed-form for $\sum_{n=0}^{\infty}\frac{n}{n^3+1}$?

Published on 26 Mar 2026 - 21:26

score 59 · Answer 2 · 2026-03-26 01:28:17

59

Views

Closed form expression for sequence of values created by differently signed series

Published on 26 Mar 2026 - 1:28

score 93 · Answer 3 · 2020-06-21 10:48:17

93

Views

Closed form of an integral that seems "alike" the Laplace integral

Published on 21 Jun 2020 - 10:48

score 32 · Answer 4 · 2020-06-22 04:14:13

32

Views

What is the closed form of the generating function of the solution to a linear recurrence?

Published on 22 Jun 2020 - 4:14

score 135 · Answer 5 · 2026-03-27 04:35:17

135

Views

Evaluating $\int_0^1\frac{\ln(1+x^2)\text{Li}_2(x)}{x}dx$ without using $\sum_{n=1}^\infty\frac{H_n}{n^3}x^n$

Published on 27 Mar 2026 - 4:35

score 413 · Answer 6 · 2026-03-27 04:38:19

413

Views

Evaluate $\int_0^1 \log (1-x)\ _3F_2\left(1,1,1;\frac{3}{2},\frac{3}{2};x\right) \, dx$

Published on 27 Mar 2026 - 4:38

score 24 · Answer 7 · 2020-06-24 10:40:39

24

Views

Product of function in closed form

Published on 24 Jun 2020 - 10:40

score 84 · Answer 8 · 2026-03-27 02:50:49

84

Views

Converting Circular formulae to Independent functions

Published on 27 Mar 2026 - 2:50

score 153 · Answer 9 · 2020-06-25 13:46:48

153

Views

Finding a closed form to a minimum of a function

Published on 25 Jun 2020 - 13:46

score 690 · Answer 10 · 2026-03-28 14:44:32

690

Views

Evaluate hypergeometric $_6F_5\left(\{\frac12\}_3,\{1\}_3;\{\frac32\}_5;1\right)$

Published on 28 Mar 2026 - 14:44

score 55 · Answer 11 · 2020-06-27 07:01:17

55

Views

Closed form of $\sum_{n=1}^\infty (n+k)!(a/n)^n$

Published on 27 Jun 2020 - 7:01

score 578 · Answer 12 · 2026-03-25 14:26:05

578

Views

Alternative approaches to showing that $\Gamma'(1/2)=-\sqrt\pi\left(\gamma+\log(4)\right)$

Published on 25 Mar 2026 - 14:26

score 202 · Answer 13 · 2020-06-27 21:29:09

202

Views

The conjecture about the existence of closed-form inverses of functions

Published on 27 Jun 2020 - 21:29

score 145 · Answer 14 · 2026-03-26 04:34:40

145

Views

Any nice (not necessarily closed) forms for ${\sum_{n=1}^{\infty}\frac{(-1)^{n+1}\eta(2n)}{n}}$?

Published on 26 Mar 2026 - 4:34

score 270 · Answer 15 · 2020-06-29 10:18:35

270

Views

Closed form expression for $\sum\limits_{k=0}^{\infty}\frac{k4^k}{n+k}{n+k\choose n-k}{n\choose k}{2n\choose 2k}^{-1}$

Published on 29 Jun 2020 - 10:18

List Question

Is there a closed-form for $\sum_{n=0}^{\infty}\frac{n}{n^3+1}$?

Closed form expression for sequence of values created by differently signed series

Closed form of an integral that seems "alike" the Laplace integral

What is the closed form of the generating function of the solution to a linear recurrence?

Evaluating $\int_0^1\frac{\ln(1+x^2)\text{Li}_2(x)}{x}dx$ without using $\sum_{n=1}^\infty\frac{H_n}{n^3}x^n$

Evaluate $\int_0^1 \log (1-x)\ _3F_2\left(1,1,1;\frac{3}{2},\frac{3}{2};x\right) \, dx$

Product of function in closed form

Converting Circular formulae to Independent functions

Finding a closed form to a minimum of a function

Evaluate hypergeometric $_6F_5\left(\{\frac12\}_3,\{1\}_3;\{\frac32\}_5;1\right)$

Closed form of $\sum_{n=1}^\infty (n+k)!(a/n)^n$

Alternative approaches to showing that $\Gamma'(1/2)=-\sqrt\pi\left(\gamma+\log(4)\right)$

The conjecture about the existence of closed-form inverses of functions

Any nice (not necessarily closed) forms for ${\sum_{n=1}^{\infty}\frac{(-1)^{n+1}\eta(2n)}{n}}$?

Closed form expression for $\sum\limits_{k=0}^{\infty}\frac{k4^k}{n+k}{n+k\choose n-k}{n\choose k}{2n\choose 2k}^{-1}$

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