Question

Closed-form expression for $\sum_{n = 0}^{\infty}(\frac{(ln(4n+3))^k}{4n+3}-\frac{(ln(4n+5))^k}{4n+5}),$ where $k$ is a positive integer

score 60 · Answer 1 · 2020-07-24 03:00:28

Closed-form expression for $\sum_{n = 0}^{\infty}(\frac{(ln(4n+3))^k}{4n+3}-\frac{(ln(4n+5))^k}{4n+5}),$ where $k$ is a positive integer

score 103 · Answer 2 · 2020-07-26 09:17:21

103

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What is the closed form of the sequence $\left\lbrace 32, 422, 3406 , 22426,131995, ... \right\rbrace$

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score 83 · Answer 3 · 2026-03-27 13:37:19

83

Views

Recursion with combinatoric argument

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score 143 · Answer 4 · 2026-03-27 22:52:38

143

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score 175 · Answer 5 · 2026-03-30 14:41:14

175

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score 177 · Answer 6 · 2026-03-29 06:07:57

177

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What is $\sum_{i=1}^{n}\frac{F_i}{i}$?

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score 397 · Answer 7 · 2016-07-06 09:52:48

397

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Does there exist a closed-form expression for the following function?

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score 143 · Answer 8 · 2026-03-27 13:39:56

143

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Evaluating $\int_1^{\infty}x\: \text{erfc}(a+b \log (x)) \, dx$

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score 195 · Answer 9 · 2016-07-08 19:01:28

195

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How do we prove that $\int_{0}^{1}\int_{0}^{1}{\left(\ln{x}\ln{y}\right)^s\over 1-xy}dxdy=\Gamma^2(1+s)\zeta(2+2s)$?

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score 144 · Answer 10 · 2016-07-08 23:33:21

144

Views

Sum to closed form

Published on 08 Jul 2016 - 23:33

score 2k · Answer 11 · 2026-03-29 18:19:56

2k

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Find the integer part of the sum $S=\sum_{k=1}^{80} \frac{1}{\sqrt k} $

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score 763 · Answer 12 · 2016-07-10 10:07:00

763

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score 104 · Answer 13 · 2016-07-10 20:10:56

104

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Closed formula for Sum

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score 379 · Answer 14 · 2026-03-27 00:05:59

379

Views

Can you help me to evaluate $\int_{-\infty}^\infty\frac{x^2}{-1+\cosh (2x)}dx$ as $\pi^2/6$? And do you find a similar integral for $\zeta(4)$?

Published on 27 Mar 2026 - 0:05

score 59 · Answer 15 · 2016-07-12 14:42:33

59

Views

Finding a limit of a two variable function: $f(x,y)=\frac {\sin(x^2-xy)}{\vert x\vert} $

Published on 12 Jul 2016 - 14:42

List Question

Closed-form expression for $\sum_{n = 0}^{\infty}(\frac{(ln(4n+3))^k}{4n+3}-\frac{(ln(4n+5))^k}{4n+5}),$ where $k$ is a positive integer

What is the closed form of the sequence $\left\lbrace 32, 422, 3406 , 22426,131995, ... \right\rbrace$

Recursion with combinatoric argument

Is there any closed-form solution for free boundary problem?

Closed-from for the series: $\sum_{k=0}^{\infty} \frac{1}{(k!)!}$

What is $\sum_{i=1}^{n}\frac{F_i}{i}$?

Does there exist a closed-form expression for the following function?

Evaluating $\int_1^{\infty}x\: \text{erfc}(a+b \log (x)) \, dx$

How do we prove that $\int_{0}^{1}\int_{0}^{1}{\left(\ln{x}\ln{y}\right)^s\over 1-xy}dxdy=\Gamma^2(1+s)\zeta(2+2s)$?

Sum to closed form

Find the integer part of the sum $S=\sum_{k=1}^{80} \frac{1}{\sqrt k} $

Evaluating $\int_0^\infty\frac{\log^{10} x}{1 +x^3}dx$

Closed formula for Sum

Can you help me to evaluate $\int_{-\infty}^\infty\frac{x^2}{-1+\cosh (2x)}dx$ as $\pi^2/6$? And do you find a similar integral for $\zeta(4)$?

Finding a limit of a two variable function: $f(x,y)=\frac {\sin(x^2-xy)}{\vert x\vert} $

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