Question

Given $\operatorname E(x,2)=a\implies x=f(a)$, what is the solution for $\operatorname E(x,2)=ia$ with elliptic integral of the second kind?

score 39 · Answer 1 · 2023-12-30 17:22:44

39

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Given $\operatorname E(x,2)=a\implies x=f(a)$, what is the solution for $\operatorname E(x,2)=ia$ with elliptic integral of the second kind?

Published on 30 Dec 2023 - 17:22

score 173 · Answer 2 · 2024-01-12 20:33:46

173

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How to reduce $\int_0^{\pi/2}\frac{\sin x(\sin x+\cos x)}{\sqrt{\sin x\cos x}}\,dx$ to complete elliptic integral?

Published on 12 Jan 2024 - 20:33

score 120 · Answer 3 · 2024-01-18 12:19:06

120

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Moments of Alternate Elliptic Integrals

Published on 18 Jan 2024 - 12:19

score 96 · Answer 4 · 2024-01-19 17:42:26

96

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Inverse of complete elliptic integral of the second kind for programmers

Published on 19 Jan 2024 - 17:42

score 158 · Answer 5 · 2024-01-22 15:30:51

158

Views

Area enclosed by the closed loop of an elliptic curve $y^2 = x^3 + a x + b$

Published on 22 Jan 2024 - 15:30

score 51 · Answer 6 · 2024-02-01 08:06:53

51

Views

How to solve integral with cubic polynomial at the denominator with Byrd-Friedman's handbook of elliptical integrals?

Published on 01 Feb 2024 - 8:06

score 160 · Answer 7 · 2024-02-02 13:46:24

160

Views

When is this indefinite integral $\int\frac{\mathrm dx}{\sqrt{x^n+1}}$ expressible in terms of elliptic integrals?

Published on 02 Feb 2024 - 13:46

score 38 · Answer 8 · 2024-02-03 23:23:37

38

Views

Deriving connection formulas for the incomplete elliptic integral of the third kind

Published on 03 Feb 2024 - 23:23

score 207 · Answer 9 · 2024-02-04 10:36:56

207

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Integrate $\int_0^1\left(\int_0^\pi \frac{u}{\sqrt{1+u^2-2u \cos\phi}} d\phi\right)du$

Published on 04 Feb 2024 - 10:36

score 137 · Answer 10 · 2024-02-13 11:03:21

137

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Series $\sum_{n=0}^{\infty}(-1)^n\binom{2n}{n}^5\left(\frac{1+4n}{2^{10n}}\right)=\frac{\Gamma^4(1/4)}{2\pi^4}$

Published on 13 Feb 2024 - 11:03

score 69 · Answer 11 · 2024-02-13 13:57:23

69

Views

Strange algebra among elliptic moments $k^pK^qK^\prime{}^r$

Published on 13 Feb 2024 - 13:57

score 94 · Answer 12 · 2026-03-25 04:00:11

94

Views

$\int_0^1E(k)dk$ without switching integrals

Published on 25 Mar 2026 - 4:00

score 669 · Answer 13 · 2024-02-16 05:05:44

669

Views

Other approaches to $\int_{0}^{1} \frac{K\left ( x \right ) }{\sqrt{3-x} } \text{d}x$

Published on 16 Feb 2024 - 5:05

score 122 · Answer 14 · 2024-02-19 19:39:14

122

Views

Ramanujan-Type Double Sum Infinite Series for $1/\pi$

Published on 19 Feb 2024 - 19:39

score 164 · Answer 15 · 2024-02-20 00:06:47

164

Views

Direct evaluation challenge of a Dedekind $\eta$ elliptic integral

Published on 20 Feb 2024 - 0:06

List Question

Given $\operatorname E(x,2)=a\implies x=f(a)$, what is the solution for $\operatorname E(x,2)=ia$ with elliptic integral of the second kind?

How to reduce $\int_0^{\pi/2}\frac{\sin x(\sin x+\cos x)}{\sqrt{\sin x\cos x}}\,dx$ to complete elliptic integral?

Moments of Alternate Elliptic Integrals

Inverse of complete elliptic integral of the second kind for programmers

Area enclosed by the closed loop of an elliptic curve $y^2 = x^3 + a x + b$

How to solve integral with cubic polynomial at the denominator with Byrd-Friedman's handbook of elliptical integrals?

When is this indefinite integral $\int\frac{\mathrm dx}{\sqrt{x^n+1}}$ expressible in terms of elliptic integrals?

Deriving connection formulas for the incomplete elliptic integral of the third kind

Integrate $\int_0^1\left(\int_0^\pi \frac{u}{\sqrt{1+u^2-2u \cos\phi}} d\phi\right)du$

Series $\sum_{n=0}^{\infty}(-1)^n\binom{2n}{n}^5\left(\frac{1+4n}{2^{10n}}\right)=\frac{\Gamma^4(1/4)}{2\pi^4}$

Strange algebra among elliptic moments $k^pK^qK^\prime{}^r$

$\int_0^1E(k)dk$ without switching integrals

Other approaches to $\int_{0}^{1} \frac{K\left ( x \right ) }{\sqrt{3-x} } \text{d}x$

Ramanujan-Type Double Sum Infinite Series for $1/\pi$

Direct evaluation challenge of a Dedekind $\eta$ elliptic integral

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