List questions from elliptic-integrals

Published on 23 Jan 2017 - 5:48

366

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A known closed form for Borchardt mean (generalization of AGM) - why doesn't it work?

Published on 27 Jan 2017 - 22:52

1.3k

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Ellipse arc length with series expansion

Published on 06 Feb 2017 - 18:55

242

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perimeter of ellipse

Published on 14 Feb 2017 - 21:25

285

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Mapping from Riemann surface to plane

Published on 02 Mar 2017 - 2:17

184

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complete elliptic integral of the 1st kind with infinitely large argument

Published on 25 Mar 2026 - 3:20

592

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Proof of an Elliptic Integral Relation

Published on 15 Mar 2017 - 14:43

409

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Jacobian Elliptic Functions

Published on 05 Apr 2017 - 12:45

294

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Prove that $\int_{0}^{1}x^2K^\prime(x)^3\text{d}x =\frac{\Gamma\left ( \frac14 \right )^8 }{640\pi^2} -\frac{\pi^4}{40}$

Published on 31 Jan 2023 - 16:37

361

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Derivation of an integral containing the complete elliptic integral of the first kind

Published on 23 Feb 2026 - 15:09

87

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Can order of summation and integral be interchanged in : $\int_{-1}^1 ( \sum_{n=0}^\infty P_n(\xi)P_n(\xi^\prime)Q_l(\xi^\prime))\text{d}\xi^\prime$?

Published on 13 Feb 2023 - 23:14

144

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Express $\sum_{n\in\mathbb{Z}} \left ( q^{(8n+1)^2}-q^{(8n+3)^2}\right )$

Published on 14 Feb 2023 - 13:36

595

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Evaluation of $\int_0^1\frac{\log x\,dx}{\sqrt{x(1-x)(1-cx)}}$

Published on 16 Feb 2023 - 16:48

153

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Are these sources wrong about Jacobi elliptic functions, and can we fix the flaw?

Published on 21 Feb 2023 - 7:02

54

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Closed form for recursive square super-roots of two numbers?

Published on 24 Feb 2023 - 23:49

List Question

Prove known closed form for $\int_0^\infty e^{-x}I_0\left(\frac{x}{3}\right)^3\;dx$

A known closed form for Borchardt mean (generalization of AGM) - why doesn't it work?

Ellipse arc length with series expansion

perimeter of ellipse

Mapping from Riemann surface to plane

complete elliptic integral of the 1st kind with infinitely large argument

Proof of an Elliptic Integral Relation

Jacobian Elliptic Functions

Prove that $\int_{0}^{1}x^2K^\prime(x)^3\text{d}x =\frac{\Gamma\left ( \frac14 \right )^8 }{640\pi^2} -\frac{\pi^4}{40}$

Derivation of an integral containing the complete elliptic integral of the first kind

Can order of summation and integral be interchanged in : $\int_{-1}^1 ( \sum_{n=0}^\infty P_n(\xi)P_n(\xi^\prime)Q_l(\xi^\prime))\text{d}\xi^\prime$?

Express $\sum_{n\in\mathbb{Z}} \left ( q^{(8n+1)^2}-q^{(8n+3)^2}\right )$

Evaluation of $\int_0^1\frac{\log x\,dx}{\sqrt{x(1-x)(1-cx)}}$

Are these sources wrong about Jacobi elliptic functions, and can we fix the flaw?

Closed form for recursive square super-roots of two numbers?

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