List questions from elliptic-integrals

Published on 19 Feb 2014 - 9:09

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The transformations on the nome and Landen's transformation

Published on 24 Feb 2014 - 22:02

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How to prove $\int_0^\pi\frac{\ln(2+\cos\phi)}{\sqrt{2+\cos\phi}}d\phi=\frac{\ln3}{\sqrt3}K\left(\sqrt{\frac23}\right)$?

Published on 27 Feb 2014 - 3:14

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How to prove $\int_1^\infty\frac{K(x)^2}x dx=\frac{i\,\pi^3}8$?

Published on 28 Feb 2014 - 22:54

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Proving Legendres Relation for elliptic curves

Published on 06 Mar 2014 - 9:32

875

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Conjecture about integral $\int_0^1 K\left(\sqrt{\vphantom1x}\right)\,K\left(\sqrt{1-x}\right)\,x^ndx$

Published on 09 Mar 2014 - 2:49

494

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A Nasty Elliptic Integral

Published on 10 Apr 2017 - 2:12

89

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How to deal with a high order integral by using the elliptic integral?

Published on 21 Apr 2017 - 14:50

323

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Imaginary part of expression involving complete elliptic integral

Published on 25 Apr 2017 - 21:16

719

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Real part of elliptic integral

Published on 26 Apr 2017 - 9:21

59

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Doing the integral, possible using some elliptic functions/integrals.

Published on 15 May 2017 - 14:14

74

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Given $|x|<1$, prove $\lim\limits_{n \to \infty} \int\limits_0^x t^n/(1+t)\ dt = 0$

Published on 17 May 2017 - 23:54

297

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An Unconventional Elliptic Integral?

Published on 18 May 2017 - 3:31

120

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Identity for the real part of the elliptic integral of the first kind: references

Published on 19 May 2017 - 13:18

95

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Möbius-Transform of Elliptic Differential

Published on 19 May 2017 - 15:08

List Question

How to integrate $ \int \frac{x}{\sqrt{x^4+10x^2-96x-71}}dx$?

The transformations on the nome and Landen's transformation

How to prove $\int_0^\pi\frac{\ln(2+\cos\phi)}{\sqrt{2+\cos\phi}}d\phi=\frac{\ln3}{\sqrt3}K\left(\sqrt{\frac23}\right)$?

How to prove $\int_1^\infty\frac{K(x)^2}x dx=\frac{i\,\pi^3}8$?

Proving Legendres Relation for elliptic curves

Conjecture about integral $\int_0^1 K\left(\sqrt{\vphantom1x}\right)\,K\left(\sqrt{1-x}\right)\,x^ndx$

A Nasty Elliptic Integral

How to deal with a high order integral by using the elliptic integral?

Imaginary part of expression involving complete elliptic integral

Real part of elliptic integral

Doing the integral, possible using some elliptic functions/integrals.

Given $|x|<1$, prove $\lim\limits_{n \to \infty} \int\limits_0^x t^n/(1+t)\ dt = 0$

An Unconventional Elliptic Integral?

Identity for the real part of the elliptic integral of the first kind: references

Möbius-Transform of Elliptic Differential

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