Question

Find a closed form for $f(x):(-1,1)\to\Bbb{R}$ defined by $\sum_{n=0}^{\infty}(-1)^{n}(n-2) x^{n}$

score 34 · Answer 1 · 2019-10-08 22:36:07

34

Views

Find a closed form for $f(x):(-1,1)\to\Bbb{R}$ defined by $\sum_{n=0}^{\infty}(-1)^{n}(n-2) x^{n}$

Published on 08 Oct 2019 - 22:36

score 51 · Answer 2 · 2019-10-09 22:54:32

51

Views

Closed formula or approximations for $\sum_{i=2}^{n} \lfloor \log_{i}(n) \rfloor$

Published on 09 Oct 2019 - 22:54

score 183 · Answer 3 · 2026-03-17 13:54:10

183

Views

Evaluate $\sum _{k=0}^{\infty } \frac{L_{2 k+1}}{(2 k+1)^2 \binom{2 k}{k}}$

Published on 17 Mar 2026 - 13:54

score 181 · Answer 4 · 2026-03-28 01:35:29

181

Views

Closed form of infinite product

Published on 28 Mar 2026 - 1:35

score 356 · Answer 5 · 2026-03-26 22:53:17

356

Views

Compute $\sum_{n=1}^{\infty} \frac{ H_{n/2}}{(2n+1)^3}$

Published on 26 Mar 2026 - 22:53

score 91 · Answer 6 · 2026-03-28 16:19:31

91

Views

Integration involving some special functions

Published on 28 Mar 2026 - 16:19

score 168 · Answer 7 · 2026-03-29 08:15:00

168

Views

$ a_n = \frac{a_{n-1}(a_{n-1} + 1)}{a_{n-2}}.$ and $ T = 3.73205080..$?

Published on 29 Mar 2026 - 8:15

score 259 · Answer 8 · 2026-03-25 23:16:35

259

Views

Closed form for $\sqrt{1+\sqrt{x+\sqrt{x^2+\sqrt{x^3+\sqrt{x^4+...}}}}}$

Published on 25 Mar 2026 - 23:16

score 91 · Answer 9 · 2019-10-17 09:37:36

91

Views

Evaluate $\sum _{n=1}^{\infty } \frac{\left(\frac{4}{9}\right)^n \beta (2 n+1)}{n+1}$

Published on 17 Oct 2019 - 9:37

score 58 · Answer 10 · 2019-10-18 13:54:01

58

Views

$\int \sqrt{\frac{1-{x}}{1+{x}}.\frac{1}{x^2}}dx$

Published on 18 Oct 2019 - 13:54

score 78 · Answer 11 · 2026-03-28 14:53:42

78

Views

Corrections to definite integral involving some special function

Published on 28 Mar 2026 - 14:53

score 42 · Answer 12 · 2019-10-20 12:01:25

42

Views

Closed form for BAPC 2019 lucky draw problem

Published on 20 Oct 2019 - 12:01

score 157 · Answer 13 · 2019-10-20 19:52:02

157

Views

$\int \frac{dx}{1-\sin x+\cos x}$

Published on 20 Oct 2019 - 19:52

score 186 · Answer 14 · 2019-10-22 02:58:36

186

Views

Evaluate $\int _0^1\int _0^1\frac{\log \left(x^2+y^2\right)}{\sqrt{x+y}}dydx$

Published on 22 Oct 2019 - 2:58

score 134 · Answer 15 · 2019-10-22 03:14:26

134

Views

Evaluation of a digamma series involving golden-ratio

Published on 22 Oct 2019 - 3:14

List Question

Find a closed form for $f(x):(-1,1)\to\Bbb{R}$ defined by $\sum_{n=0}^{\infty}(-1)^{n}(n-2) x^{n}$

Closed formula or approximations for $\sum_{i=2}^{n} \lfloor \log_{i}(n) \rfloor$

Evaluate $\sum _{k=0}^{\infty } \frac{L_{2 k+1}}{(2 k+1)^2 \binom{2 k}{k}}$

Closed form of infinite product

Compute $\sum_{n=1}^{\infty} \frac{ H_{n/2}}{(2n+1)^3}$

Integration involving some special functions

$ a_n = \frac{a_{n-1}(a_{n-1} + 1)}{a_{n-2}}.$ and $ T = 3.73205080..$?

Closed form for $\sqrt{1+\sqrt{x+\sqrt{x^2+\sqrt{x^3+\sqrt{x^4+...}}}}}$

Evaluate $\sum _{n=1}^{\infty } \frac{\left(\frac{4}{9}\right)^n \beta (2 n+1)}{n+1}$

$\int \sqrt{\frac{1-{x}}{1+{x}}.\frac{1}{x^2}}dx$

Corrections to definite integral involving some special function

Closed form for BAPC 2019 lucky draw problem

$\int \frac{dx}{1-\sin x+\cos x}$

Evaluate $\int _0^1\int _0^1\frac{\log \left(x^2+y^2\right)}{\sqrt{x+y}}dydx$

Evaluation of a digamma series involving golden-ratio

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