Question

Improper Integral Involving Hyperbolic Cotangent

score 230 · Answer 1 · 2026-04-11 06:15:47

230

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Improper Integral Involving Hyperbolic Cotangent

Published on 11 Apr 2026 - 6:15

score 240 · Answer 2 · 2021-12-27 13:18:41

240

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Evaluate $\int_{0}^{\pi/2}\left [\text{ Ci}(\alpha\sin\theta)^2+\left(\frac{\pi}{2}-\text{ Si}(\alpha\sin\theta)\right)^2\right ]\text{d}\theta$

Published on 27 Dec 2021 - 13:18

score 239 · Answer 3 · 2021-12-31 11:19:16

239

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Evaluate some integrals with hypergeometric function

Published on 31 Dec 2021 - 11:19

score 175 · Answer 4 · 2022-01-04 07:33:14

175

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Closed form of $\sum\limits^\infty_{n=1} \left( {(-1)^n}\left( 1+n\ln(\frac{2n-1}{2n+1}) \right) \right)$

Published on 04 Jan 2022 - 7:33

score 63 · Answer 5 · 2026-04-13 07:06:01

63

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Understanding special functions

Published on 13 Apr 2026 - 7:06

score 651 · Answer 6 · 2026-04-09 12:13:10

651

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Proof of sum with Bernoulli poly: $\frac{(-1)^{n+1}}{2}\sum_{k=0}^{n-1} \binom{n-1}{j} B_{n+j}(1/2) \frac{1}{n+j} =4^{-n}-\frac{1}{2n\binom{2n}{n}}$

Published on 09 Apr 2026 - 12:13

score 85 · Answer 7 · 2026-04-12 01:37:30

85

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Does a closed form expression of this series exist?

Published on 12 Apr 2026 - 1:37

score 120 · Answer 8 · 2026-03-30 20:52:58

120

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Computing $A=\sum_{k=0}^{\infty}\frac{\alpha(\alpha+k\beta)^{k-1}e^{-(\alpha+k\beta)}}{k!}f^{k}$

Published on 30 Mar 2026 - 20:52

score 78 · Answer 9 · 2026-04-10 12:13:11

78

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Sum of terms in closed form

Published on 10 Apr 2026 - 12:13

score 481 · Answer 10 · 2026-03-25 10:25:08

481

Views

Finding $\int_{1}^{\infty} \frac{1}{1+x^2} \frac{\operatorname{Li}_2\left ( \frac{1-x}{2} \right ) }{\pi^2+\ln^2\left(\frac{x-1}{2}\right)}\text{d}x$

Published on 25 Mar 2026 - 10:25

score 1.1k · Answer 11 · 2026-04-11 04:00:39

1.1k

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A rare integral involving $\operatorname{Li}_2$

Published on 11 Apr 2026 - 4:00

score 763 · Answer 12 · 2026-04-12 05:15:40

763

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A generalized "Rare" integral involving $\operatorname{Li}_3$

Published on 12 Apr 2026 - 5:15

score 223 · Answer 13 · 2026-04-12 12:56:33

223

Views

Closed form expression for series involving Legendre polynomials

Published on 12 Apr 2026 - 12:56

score 58 · Answer 14 · 2026-04-06 03:44:30

58

Views

Closed form for $\prod_{j=1}^n\prod_{k=1}^{m_{j}-1} (x_j-kN^{-1})$

Published on 06 Apr 2026 - 3:44

score 229 · Answer 15 · 2022-01-30 11:42:02

229

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Evaluate $\int_{0}^{\infty }\!{\frac {\ln \left( x \right) \arctan \left( x \right) }{{{\rm e}^{\pi\,x}}-1}}\,{\rm d}x$

Published on 30 Jan 2022 - 11:42

List Question

Improper Integral Involving Hyperbolic Cotangent

Evaluate $\int_{0}^{\pi/2}\left [\text{ Ci}(\alpha\sin\theta)^2+\left(\frac{\pi}{2}-\text{ Si}(\alpha\sin\theta)\right)^2\right ]\text{d}\theta$

Evaluate some integrals with hypergeometric function

Closed form of $\sum\limits^\infty_{n=1} \left( {(-1)^n}\left( 1+n\ln(\frac{2n-1}{2n+1}) \right) \right)$

Understanding special functions

Proof of sum with Bernoulli poly: $\frac{(-1)^{n+1}}{2}\sum_{k=0}^{n-1} \binom{n-1}{j} B_{n+j}(1/2) \frac{1}{n+j} =4^{-n}-\frac{1}{2n\binom{2n}{n}}$

Does a closed form expression of this series exist?

Computing $A=\sum_{k=0}^{\infty}\frac{\alpha(\alpha+k\beta)^{k-1}e^{-(\alpha+k\beta)}}{k!}f^{k}$

Sum of terms in closed form

Finding $\int_{1}^{\infty} \frac{1}{1+x^2} \frac{\operatorname{Li}_2\left ( \frac{1-x}{2} \right ) }{\pi^2+\ln^2\left(\frac{x-1}{2}\right)}\text{d}x$

A rare integral involving $\operatorname{Li}_2$

A generalized "Rare" integral involving $\operatorname{Li}_3$

Closed form expression for series involving Legendre polynomials

Closed form for $\prod_{j=1}^n\prod_{k=1}^{m_{j}-1} (x_j-kN^{-1})$

Evaluate $\int_{0}^{\infty }\!{\frac {\ln \left( x \right) \arctan \left( x \right) }{{{\rm e}^{\pi\,x}}-1}}\,{\rm d}x$

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