Question

How to convert $\frac{1}{2\pi}\int_{0}^{2\pi}\sqrt{(ucos(\theta)+v\sin(\theta))^2-(u^2+v^2-1)} d\theta$ to an elliptic integral?

score 152 · Answer 1 · 2026-03-23 00:34:43

152

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How to convert $\frac{1}{2\pi}\int_{0}^{2\pi}\sqrt{(ucos(\theta)+v\sin(\theta))^2-(u^2+v^2-1)} d\theta$ to an elliptic integral?

Published on 23 Mar 2026 - 0:34

score 335 · Answer 2 · 2026-03-22 10:05:41

335

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Finding zeros of the elliptic function $f(z) = \sum_{\omega \in \Omega} \frac{1}{(z - \omega)^3}$

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score 1.4k · Answer 3 · 2026-03-22 14:47:20

1.4k

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score 1k · Answer 4 · 2026-03-22 21:41:10

1k

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score 232 · Answer 5 · 2026-03-22 15:18:10

232

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score 168 · Answer 6 · 2026-03-22 23:27:07

168

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score 104 · Answer 7 · 2026-03-22 20:19:26

104

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score 145 · Answer 8 · 2026-03-21 13:56:22

145

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score 136 · Answer 9 · 2026-03-22 16:08:57

136

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score 644 · Answer 10 · 2026-03-23 00:44:18

644

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score 180 · Answer 11 · 2026-03-22 10:44:11

180

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score 65 · Answer 12 · 2026-03-24 22:08:10

65

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211

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score 70 · Answer 14 · 2026-03-24 18:41:26

70

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score 334 · Answer 15 · 2026-03-25 01:13:11

334

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List Question

How to convert $\frac{1}{2\pi}\int_{0}^{2\pi}\sqrt{(ucos(\theta)+v\sin(\theta))^2-(u^2+v^2-1)} d\theta$ to an elliptic integral?

Finding zeros of the elliptic function $f(z) = \sum_{\omega \in \Omega} \frac{1}{(z - \omega)^3}$

Calculating derivatives of the Weierstrass $\wp$-function in terms of $\wp$ and $\wp '$

Dimension of space of meromorphic functions on torus with only one pole

Extension of a conformal mapping to an elliptic function

Can a polynomial be expressed as a rational function in Weierstrass functions?

Integer solutions of $ax^3 + bx^2 + cx - y^2 = k$

Meromorphic Functions that satisfy a first order algebraic differential equation

ODE and elliptic function (Pendulum)

Do we have a conformal mapping from the regular pentagon to the disk?

Jacobi form to Weierstrass form . . . lattices included .... polynomial factoring in the way

How to transfer integral to elliptic one

Doubly Periodic Entire Functions

Methods for coupled differential equations with elliptic functions

Conversion to elliptic integrals

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