Question

Is there a closed form expression for the sum of the reciprocal values of the first n natural numbers?

score 264 · Answer 1 · 2017-05-10 14:19:18

264

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Is there a closed form expression for the sum of the reciprocal values of the first n natural numbers?

Published on 10 May 2017 - 14:19

score 165 · Answer 2 · 2026-03-28 11:33:32

165

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How do we evaluate the closed form for $\int_{-\infty}^{+\infty}{(-1)^{n+1}x^{2n}+2n+1\over (1+x^2)^2}\cdot e^{-x^2}\mathrm dx?$

Published on 28 Mar 2026 - 11:33

score 252 · Answer 3 · 2017-05-16 16:05:48

252

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How to evaluate the closed form for $\int_{0}^{\pi/2}{\mathrm dx\over \sin^2(x)}\ln\left({a+b\sin^2(x)\over a-b\sin^2(x)}\right)=\pi\cdot F(a,b)?$

Published on 16 May 2017 - 16:05

score 270 · Answer 4 · 2017-05-17 04:52:56

270

Views

How can we determine the closed form for $\int_{0}^{\infty}{\ln(e^x-1)\over e^x+1}\mathrm dx?$

Published on 17 May 2017 - 4:52

score 178 · Answer 5 · 2017-05-17 12:15:16

178

Views

How to find the closed form for this polynomial generating function with 2 variables

Published on 17 May 2017 - 12:15

score 205 · Answer 6 · 2017-05-17 14:45:35

205

Views

How to evaluate $\int_{0}^{\infty}{\ln(x)\over x}\left({1+x+e^x\over e^x+e^{2x}}-{1\over \sqrt{1+ x^2}}\right)\mathrm dx?$

Published on 17 May 2017 - 14:45

score 427 · Answer 7 · 2017-05-17 18:14:51

427

Views

Defining a repeating series with a simple expression.

Published on 17 May 2017 - 18:14

score 220 · Answer 8 · 2026-04-08 04:09:54

220

Views

Closed Form Solution to Difficult Integral

Published on 08 Apr 2026 - 4:09

score 352 · Answer 9 · 2026-03-26 14:26:35

352

Views

Closed form solution to exponential equation

Published on 26 Mar 2026 - 14:26

score 491 · Answer 10 · 2017-05-26 11:47:48

491

Views

Compute $\int_0^\frac {\pi} {2} \frac {\cos x}{(1+\sqrt{\sin (2x)})^2}\,dx$

Published on 26 May 2017 - 11:47

score 80 · Answer 11 · 2017-05-26 21:02:03

80

Views

How can i find closed-form expressoin of this recursive relation?

Published on 26 May 2017 - 21:02

score 113 · Answer 12 · 2017-05-26 21:28:38

113

Views

Closed-form expression of generating function of this series

Published on 26 May 2017 - 21:28

score 1.4k · Answer 13 · 2017-05-26 21:59:50

1.4k

Views

How to find closed-form expression of this series?

Published on 26 May 2017 - 21:59

score 139 · Answer 14 · 2017-05-28 08:04:48

139

Views

How to evaluate the closed form of $I=\int_{0}^{1}\ln[\sin(\pi x)]\ln^2[2\sin(\pi x)]\mathrm dx?$

Published on 28 May 2017 - 8:04

score 445 · Answer 15 · 2017-06-01 12:59:18

445

Views

Closed form for $\int_{0}^{2\pi} e^{\sin(x)+\cos(x)} dx$

Published on 01 Jun 2017 - 12:59

List Question

Is there a closed form expression for the sum of the reciprocal values of the first n natural numbers?

How do we evaluate the closed form for $\int_{-\infty}^{+\infty}{(-1)^{n+1}x^{2n}+2n+1\over (1+x^2)^2}\cdot e^{-x^2}\mathrm dx?$

How to evaluate the closed form for $\int_{0}^{\pi/2}{\mathrm dx\over \sin^2(x)}\ln\left({a+b\sin^2(x)\over a-b\sin^2(x)}\right)=\pi\cdot F(a,b)?$

How can we determine the closed form for $\int_{0}^{\infty}{\ln(e^x-1)\over e^x+1}\mathrm dx?$

How to find the closed form for this polynomial generating function with 2 variables

How to evaluate $\int_{0}^{\infty}{\ln(x)\over x}\left({1+x+e^x\over e^x+e^{2x}}-{1\over \sqrt{1+ x^2}}\right)\mathrm dx?$

Defining a repeating series with a simple expression.

Closed Form Solution to Difficult Integral

Closed form solution to exponential equation

Compute $\int_0^\frac {\pi} {2} \frac {\cos x}{(1+\sqrt{\sin (2x)})^2}\,dx$

How can i find closed-form expressoin of this recursive relation?

Closed-form expression of generating function of this series

How to find closed-form expression of this series?

How to evaluate the closed form of $I=\int_{0}^{1}\ln[\sin(\pi x)]\ln^2[2\sin(\pi x)]\mathrm dx?$

Closed form for $\int_{0}^{2\pi} e^{\sin(x)+\cos(x)} dx$

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