Question

Evaluating series of zeta values like $\sum_{k=1}^{\infty} \frac{\zeta(2k)}{k16^{k}}=\ln(\pi)-\frac{3}{2}\ln(2) $

score 405 · Answer 1 · 2016-07-12 19:40:01

405

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Evaluating series of zeta values like $\sum_{k=1}^{\infty} \frac{\zeta(2k)}{k16^{k}}=\ln(\pi)-\frac{3}{2}\ln(2) $

Published on 12 Jul 2016 - 19:40

score 216 · Answer 2 · 2016-07-14 17:28:02

216

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Closed form of function $f(n) = \frac1n \sum\limits _{k=1}^{n-1} f(k)$?

Published on 14 Jul 2016 - 17:28

score 244 · Answer 3 · 2016-07-14 19:54:47

244

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A closed form of the series $ \sum_{n=1}^{\infty} q^n \sin(n\alpha) $

Published on 14 Jul 2016 - 19:54

score 295 · Answer 4 · 2016-07-15 06:06:25

295

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Help with $\int_0^\infty x^me^{-ax^n}dx$

Published on 15 Jul 2016 - 6:06

score 203 · Answer 5 · 2016-07-15 17:21:17

203

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A limit using the Euler number: $\lim_{n\rightarrow\infty}\frac{n!}{(n-i)!}\left(\frac{c}{n}\right)^{n-i}$

Published on 15 Jul 2016 - 17:21

score 491 · Answer 6 · 2016-07-16 05:07:02

491

Views

Problem concerning the sequence $s_n = 1 + 1/2 +\cdots+ 1/n - \log n$

Published on 16 Jul 2016 - 5:07

score 382 · Answer 7 · 2016-07-16 05:08:59

382

Views

How evaluating $\int_0^2 f(x)dx$ from $\int_2^3 f(x)dx$ and $\int_1^2xf(x^2-1)dx$?

Published on 16 Jul 2016 - 5:08

score 53 · Answer 8 · 2026-03-31 07:05:06

53

Views

Finding functions that give nice solutions to a recurrence relation.

Published on 31 Mar 2026 - 7:05

score 125 · Answer 9 · 2016-07-16 08:12:14

125

Views

Help with the integral $\int x\sqrt{\frac{1-x^2}{1+x^2}}dx$

Published on 16 Jul 2016 - 8:12

score 188 · Answer 10 · 2016-07-17 03:33:13

188

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Closed Form Expressions: Summation and Product Operators

Published on 17 Jul 2016 - 3:33

score 157 · Answer 11 · 2016-07-17 06:12:41

157

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Evaluating $\int_{s^{-1/n}}^{\infty}v^2\exp{\left[-\left(\frac{l}{v} + m v\right)^2\right]}dv$

Published on 17 Jul 2016 - 6:12

score 143 · Answer 12 · 2016-07-17 09:57:35

143

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$\lim_{z\to -1} (z+1) \sin(\frac{1}{z+1})$, for complex variable $z$.

Published on 17 Jul 2016 - 9:57

score 115 · Answer 13 · 2016-07-17 13:02:23

115

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How to prove $\ln{6}=\sum_{n=1}^{\infty}\sum_{r=2}^{\infty}\left({1\over r^{2n}}+{2\over (r+1)^{2n}}+{1\over (r+2)^{2n}}\right)$?

Published on 17 Jul 2016 - 13:02

score 303 · Answer 14 · 2016-07-18 15:17:54

303

Views

Summation of $\sum_{n=0}^\infty e^{-\sqrt n}$

Published on 18 Jul 2016 - 15:17

score 59 · Answer 15 · 2016-07-18 17:10:14

59

Views

Finding $\lim_{n\to \infty} \frac{1}{n} \sum_{k=1}^n \frac{a^{1+\frac{k}{n}}}{a^{1+\frac{k}{n}}+1} $

Published on 18 Jul 2016 - 17:10

List Question

Evaluating series of zeta values like $\sum_{k=1}^{\infty} \frac{\zeta(2k)}{k16^{k}}=\ln(\pi)-\frac{3}{2}\ln(2) $

Closed form of function $f(n) = \frac1n \sum\limits _{k=1}^{n-1} f(k)$?

A closed form of the series $ \sum_{n=1}^{\infty} q^n \sin(n\alpha) $

Help with $\int_0^\infty x^me^{-ax^n}dx$

A limit using the Euler number: $\lim_{n\rightarrow\infty}\frac{n!}{(n-i)!}\left(\frac{c}{n}\right)^{n-i}$

Problem concerning the sequence $s_n = 1 + 1/2 +\cdots+ 1/n - \log n$

How evaluating $\int_0^2 f(x)dx$ from $\int_2^3 f(x)dx$ and $\int_1^2xf(x^2-1)dx$?

Finding functions that give nice solutions to a recurrence relation.

Help with the integral $\int x\sqrt{\frac{1-x^2}{1+x^2}}dx$

Closed Form Expressions: Summation and Product Operators

Evaluating $\int_{s^{-1/n}}^{\infty}v^2\exp{\left[-\left(\frac{l}{v} + m v\right)^2\right]}dv$

$\lim_{z\to -1} (z+1) \sin(\frac{1}{z+1})$, for complex variable $z$.

How to prove $\ln{6}=\sum_{n=1}^{\infty}\sum_{r=2}^{\infty}\left({1\over r^{2n}}+{2\over (r+1)^{2n}}+{1\over (r+2)^{2n}}\right)$?

Summation of $\sum_{n=0}^\infty e^{-\sqrt n}$

Finding $\lim_{n\to \infty} \frac{1}{n} \sum_{k=1}^n \frac{a^{1+\frac{k}{n}}}{a^{1+\frac{k}{n}}+1} $

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