Question

Sums of the form $S_k=\sum_{n\geq 1}\frac{1}{\sinh^{2k}(n \pi)}$ and the residue theorem.

score 378 · Answer 1 · 2017-05-21 16:08:54

378

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Sums of the form $S_k=\sum_{n\geq 1}\frac{1}{\sinh^{2k}(n \pi)}$ and the residue theorem.

Published on 21 May 2017 - 16:08

score 224 · Answer 2 · 2026-03-27 05:39:22

224

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How to evaluate $\int_0^{\pi/2}(\sin^2\theta+a)^{-3/2}\,d\theta$, where $a>0$

Published on 27 Mar 2026 - 5:39

score 146 · Answer 3 · 2017-06-05 22:09:25

146

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limit of the derivative of ArcCos(Jacobi elliptic sine function)

Published on 05 Jun 2017 - 22:09

score 161 · Answer 4 · 2017-06-09 16:49:16

161

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Prove that $\int_0^{\pi/2}\frac{2-(4+a)\sin^2(x) - 2 a \sin^4(x)-a^2\sin^6(x)}{(1+a\sin^2(x))^{5/2}}dx=0$

Published on 09 Jun 2017 - 16:49

score 126 · Answer 5 · 2017-06-11 06:01:00

126

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Can $\int_{0}^{\infty}\frac{dx}{\sqrt[\leftroot{-1}\uproot{1}n]{x(x+a^n)(x+1)^{n-1}}}$ be expressed with an elliptic integral?

Published on 11 Jun 2017 - 6:01

score 71 · Answer 6 · 2017-06-14 13:50:08

71

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Elliptic Type Integral

Published on 14 Jun 2017 - 13:50

score 119 · Answer 7 · 2017-06-14 23:06:48

119

Views

Double Elliptic Type Integral

Published on 14 Jun 2017 - 23:06

score 289 · Answer 8 · 2026-03-27 07:17:02

289

Views

Series expansion of Elliptic integral $F(\sin^{-1}(1-x)|-1)$ where $0<x\ll1$

Published on 27 Mar 2026 - 7:17

score 559 · Answer 9 · 2017-06-28 22:54:17

559

Views

A curve with arc length equal to the elliptic integral of the first kind. What's the area?

Published on 28 Jun 2017 - 22:54

score 547 · Answer 10 · 2017-06-30 12:01:59

547

Views

Elliptic integral of the first kind as conformal mapping

Published on 30 Jun 2017 - 12:01

score 78 · Answer 11 · 2017-07-20 20:17:41

78

Views

Equality of two elliptics integrals

Published on 20 Jul 2017 - 20:17

score 367 · Answer 12 · 2026-03-27 05:42:01

367

Views

Expansion of Complete Elliptic Integral of the First Kind about the Branch Point

Published on 27 Mar 2026 - 5:42

score 1.1k · Answer 13 · 2017-08-08 20:21:38

1.1k

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Can $\Gamma(1/5)$ be written in this form?

Published on 08 Aug 2017 - 20:21

score 991 · Answer 14 · 2017-08-12 12:04:06

991

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Evaluation of complete elliptic integrals $K(k) $ for $k=\tan(\pi/8),\sin(\pi/12)$

Published on 12 Aug 2017 - 12:04

score 553 · Answer 15 · 2017-08-14 22:53:42

553

Views

Elliptic Integrals & Gamma Functions of Rational values.

Published on 14 Aug 2017 - 22:53

List Question

Sums of the form $S_k=\sum_{n\geq 1}\frac{1}{\sinh^{2k}(n \pi)}$ and the residue theorem.

How to evaluate $\int_0^{\pi/2}(\sin^2\theta+a)^{-3/2}\,d\theta$, where $a>0$

limit of the derivative of ArcCos(Jacobi elliptic sine function)

Prove that $\int_0^{\pi/2}\frac{2-(4+a)\sin^2(x) - 2 a \sin^4(x)-a^2\sin^6(x)}{(1+a\sin^2(x))^{5/2}}dx=0$

Can $\int_{0}^{\infty}\frac{dx}{\sqrt[\leftroot{-1}\uproot{1}n]{x(x+a^n)(x+1)^{n-1}}}$ be expressed with an elliptic integral?

Elliptic Type Integral

Double Elliptic Type Integral

Series expansion of Elliptic integral $F(\sin^{-1}(1-x)|-1)$ where $0<x\ll1$

A curve with arc length equal to the elliptic integral of the first kind. What's the area?

Elliptic integral of the first kind as conformal mapping

Equality of two elliptics integrals

Expansion of Complete Elliptic Integral of the First Kind about the Branch Point

Can $\Gamma(1/5)$ be written in this form?

Evaluation of complete elliptic integrals $K(k) $ for $k=\tan(\pi/8),\sin(\pi/12)$

Elliptic Integrals & Gamma Functions of Rational values.

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