List questions from elliptic-integrals

Published on 17 Oct 2023 - 10:57

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Can an ellipse have integer values for perimeter and area?

Published on 27 Oct 2023 - 20:47

129

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Integrating $\int \frac{d\theta}{\sqrt{a-b \sin \theta}}$

Published on 23 Feb 2026 - 5:31

315

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Values for which $\frac{K(k')}{K(k)}=a+i$ where $a$ is an algebraic number.

Published on 01 Nov 2023 - 18:52

211

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Proving $\sum_{n=0}^{\infty}\frac{1}{2^{n}}\sum_{r=0}^{n}\frac{1}{2^{4r}}\binom{2r}{r}^2=\frac{1}{\pi\sqrt{\pi}}\Gamma\left(\frac{1}{4}\right)^2$

Published on 03 Nov 2023 - 10:56

170

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How to evaluate $\int \frac{1}{\sqrt{x^{4}+3x^{2}+2}}dx$?

Published on 07 Nov 2023 - 5:27

81

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Solve parameterized line integral

Published on 13 Nov 2023 - 14:52

27

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Showing equivalence of Schwarz Christoffel Formula and elliptic integrals of the first kind.

Published on 15 Nov 2023 - 10:21

44

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One body problem: position as function of time

Published on 25 Mar 2026 - 9:53

89

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Is $\int \operatorname{sn}^2u\,\mathrm du$ really irreducible?

Published on 22 Nov 2023 - 9:34

425

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Ramanujan-Type Harmonic Series $\sum_{r=0}^{\infty}\binom{2r}{r}^3\left(\frac{1/6+r}{2^{8r}}\right)H_{r-1/2}=-\frac{8\ln2}{9\pi}$

Published on 25 Nov 2023 - 13:50

48

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Integrals of (Jacobi) elliptic functions

Published on 26 Mar 2026 - 9:16

371

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Integral related to $\frac{\sqrt{2}K(\sqrt{\frac{2k}{1+k}})}{\sqrt{1+k}}$.

Published on 10 Dec 2023 - 10:34

309

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Approximations to elliptic integrals

Published on 16 Dec 2023 - 3:21

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$\int\limits_0^1{\frac{{E\left( {\sqrt{\frac{t}{{1+t}}}}\right)-K\left({\sqrt{\frac{t}{{1+t}}}}\right)}}{{t\sqrt {1+t} }}}\ln \left( {1 - t}\right)dt$

Published on 21 Dec 2023 - 2:43

List Question

Integrals involving the incomplete elliptic integral of the first kind.

Can an ellipse have integer values for perimeter and area?

Integrating $\int \frac{d\theta}{\sqrt{a-b \sin \theta}}$

Values for which $\frac{K(k')}{K(k)}=a+i$ where $a$ is an algebraic number.

Proving $\sum_{n=0}^{\infty}\frac{1}{2^{n}}\sum_{r=0}^{n}\frac{1}{2^{4r}}\binom{2r}{r}^2=\frac{1}{\pi\sqrt{\pi}}\Gamma\left(\frac{1}{4}\right)^2$

How to evaluate $\int \frac{1}{\sqrt{x^{4}+3x^{2}+2}}dx$?

Solve parameterized line integral

Showing equivalence of Schwarz Christoffel Formula and elliptic integrals of the first kind.

One body problem: position as function of time

Is $\int \operatorname{sn}^2u\,\mathrm du$ really irreducible?

Ramanujan-Type Harmonic Series $\sum_{r=0}^{\infty}\binom{2r}{r}^3\left(\frac{1/6+r}{2^{8r}}\right)H_{r-1/2}=-\frac{8\ln2}{9\pi}$

Integrals of (Jacobi) elliptic functions

Integral related to $\frac{\sqrt{2}K(\sqrt{\frac{2k}{1+k}})}{\sqrt{1+k}}$.

Approximations to elliptic integrals

$\int\limits_0^1{\frac{{E\left( {\sqrt{\frac{t}{{1+t}}}}\right)-K\left({\sqrt{\frac{t}{{1+t}}}}\right)}}{{t\sqrt {1+t} }}}\ln \left( {1 - t}\right)dt$

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