Question

the integral similar to elliptic integral with upper limit is π instead of π/2

score 85 · Answer 1 · 2022-12-02 09:50:34

85

Views

the integral similar to elliptic integral with upper limit is π instead of π/2

Published on 02 Dec 2022 - 9:50

score 106 · Answer 2 · 2022-12-07 00:41:37

106

Views

Seeking elegant proof of $\sum_{cyc}\cot(x-y)\cot(y-z)=1$

Published on 07 Dec 2022 - 0:41

score 209 · Answer 3 · 2022-12-11 07:37:17

209

Views

Prove $\int_0^{\pi/2}\frac{1}{\sqrt{(1+t)^2-4t\sin^2{u}}}du \equiv \int_0^{\pi/2}\frac{1}{\sqrt{1-t^2\sin^2{u}}}du$ for $0<t<1$.

Published on 11 Dec 2022 - 7:37

score 82 · Answer 4 · 2022-12-11 13:29:48

82

Views

Could a transformation of a hyperelliptic integral related to cubic AGM be proved by substitution?

Published on 11 Dec 2022 - 13:29

score 54 · Answer 5 · 2022-12-15 21:34:03

54

Views

How exactly can we write an incomplete elliptic integral of the first kind as a sum of real and imaginary parts?

Published on 15 Dec 2022 - 21:34

score 152 · Answer 6 · 2026-03-26 20:16:58

152

Views

Properties about an elliptic integral of the first kind.

Published on 26 Mar 2026 - 20:16

score 130 · Answer 7 · 2022-12-16 18:49:45

130

Views

How can I evaluate $\int_0^1\frac{dx}{\sqrt{ax^4-3x^2+1}}$?

Published on 16 Dec 2022 - 18:49

score 147 · Answer 8 · 2022-12-22 21:41:50

147

Views

Limit of an elliptic integral

Published on 22 Dec 2022 - 21:41

score 119 · Answer 9 · 2026-03-25 06:04:32

119

Views

Asymptotics of $j$-invariant at elliptic fixed points of $\text{PSL}(2,\mathbb Z)$

Published on 25 Mar 2026 - 6:04

score 530 · Answer 10 · 2023-01-11 15:01:17

530

Views

Prove the closed-form of $\int_{0}^{1}\frac{K^\prime\left (\frac{1-x^2}{2}\right)}{\sqrt{1+x^2}}\text{d}x$

Published on 11 Jan 2023 - 15:01

score 112 · Answer 11 · 2023-01-16 16:44:16

112

Views

Show that $\int_{0}^{1}K^\prime(x)^5\text{d}x =\int_{0}^{1}(74x^2-68x+14)K(x)^5\text{d}x$

Published on 16 Jan 2023 - 16:44

score 493 · Answer 12 · 2023-01-17 15:26:58

493

Views

Evaluate $\int_{0}^{1}\frac{K(x)\ln\left(1-x^2\right)}{\sqrt{1-x^2}}\text{d}x,\int_{0}^{1}\frac{xK(x)^2\ln\left(1-x^2\right)}{\sqrt{1-x^2}}\text{d}x$

Published on 17 Jan 2023 - 15:26

score 50 · Answer 13 · 2023-01-19 09:02:22

50

Views

How can I show that $K(i)E(i)-K(i)^2=\pi/4$?

Published on 19 Jan 2023 - 9:02

score 303 · Answer 14 · 2023-01-20 07:04:25

303

Views

Evaluate $\int_{0}^{1}K\left ( \sqrt{1-x^2} \right ) K\left ( \sqrt{1-x^4} \right )\text{d}x$

Published on 20 Jan 2023 - 7:04

score 359 · Answer 15 · 2026-03-26 22:54:11

359

Views

Prove a relation between Theta functions and their derivatives to prove $\sum_{n=-\infty}^\infty \frac{1}{\cosh^2(\pi n )}$

Published on 26 Mar 2026 - 22:54

List Question

the integral similar to elliptic integral with upper limit is π instead of π/2

Seeking elegant proof of $\sum_{cyc}\cot(x-y)\cot(y-z)=1$

Prove $\int_0^{\pi/2}\frac{1}{\sqrt{(1+t)^2-4t\sin^2{u}}}du \equiv \int_0^{\pi/2}\frac{1}{\sqrt{1-t^2\sin^2{u}}}du$ for $0<t<1$.

Could a transformation of a hyperelliptic integral related to cubic AGM be proved by substitution?

How exactly can we write an incomplete elliptic integral of the first kind as a sum of real and imaginary parts?

Properties about an elliptic integral of the first kind.

How can I evaluate $\int_0^1\frac{dx}{\sqrt{ax^4-3x^2+1}}$?

Limit of an elliptic integral

Asymptotics of $j$-invariant at elliptic fixed points of $\text{PSL}(2,\mathbb Z)$

Prove the closed-form of $\int_{0}^{1}\frac{K^\prime\left (\frac{1-x^2}{2}\right)}{\sqrt{1+x^2}}\text{d}x$

Show that $\int_{0}^{1}K^\prime(x)^5\text{d}x =\int_{0}^{1}(74x^2-68x+14)K(x)^5\text{d}x$

Evaluate $\int_{0}^{1}\frac{K(x)\ln\left(1-x^2\right)}{\sqrt{1-x^2}}\text{d}x,\int_{0}^{1}\frac{xK(x)^2\ln\left(1-x^2\right)}{\sqrt{1-x^2}}\text{d}x$

How can I show that $K(i)E(i)-K(i)^2=\pi/4$?

Evaluate $\int_{0}^{1}K\left ( \sqrt{1-x^2} \right ) K\left ( \sqrt{1-x^4} \right )\text{d}x$

Prove a relation between Theta functions and their derivatives to prove $\sum_{n=-\infty}^\infty \frac{1}{\cosh^2(\pi n )}$

Trending Questions

Popular # Hahtags

Popular Questions