Question

Is there a general relationship between definite integrals over functions involving the complete elliptic integral of the first kind and zeta values?

score 215 · Answer 1 · 2022-08-11 13:35:57

215

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Is there a general relationship between definite integrals over functions involving the complete elliptic integral of the first kind and zeta values?

Published on 11 Aug 2022 - 13:35

score 277 · Answer 2 · 2026-03-28 02:10:40

277

Views

Euler's derivation of Lemniscate addition theorem

Published on 28 Mar 2026 - 2:10

score 70 · Answer 3 · 2026-03-28 02:09:29

70

Views

How to integrate Elliptic function with gaussian kernel

Published on 28 Mar 2026 - 2:09

score 78 · Answer 4 · 2022-08-16 05:45:04

78

Views

Simplifying indefinite integral (possibly in terms of elliptic integrals)

Published on 16 Aug 2022 - 5:45

score 101 · Answer 5 · 2022-09-01 15:55:54

101

Views

Find the integral for equation

Published on 01 Sep 2022 - 15:55

score 125 · Answer 6 · 2026-03-28 06:07:53

125

Views

Classification of integrals not expressible in elementary functions?

Published on 28 Mar 2026 - 6:07

score 242 · Answer 7 · 2022-10-22 04:21:22

242

Views

Periods and $\mathscr{P}(w)$ of the elliptic curve $y^2=4(x-1)(x-2)(x-3)$

Published on 22 Oct 2022 - 4:21

score 55 · Answer 8 · 2022-10-23 01:07:01

55

Views

Logarithmic Term in Elliptic Integral Expansion from Tonelli's Theorem

Published on 23 Oct 2022 - 1:07

score 64 · Answer 9 · 2022-10-30 01:03:46

64

Views

Are there tricks to calcualte the complete elliptic integral the third kind fast?

Published on 30 Oct 2022 - 1:03

score 288 · Answer 10 · 2026-02-23 06:35:38

288

Views

Show that the two elliptic integrals are equal

Published on 23 Feb 2026 - 6:35

score 41 · Answer 11 · 2026-03-25 19:01:28

41

Views

Jacobi's substitution for modular equations

Published on 25 Mar 2026 - 19:01

score 63 · Answer 12 · 2026-03-25 20:33:53

63

Views

Connection between modular equation and elliptic integral

Published on 25 Mar 2026 - 20:33

score 111 · Answer 13 · 2022-11-19 12:08:50

111

Views

What is the value of $\int_{\sqrt{3}}^{2}\sqrt{y^2-3}\sqrt{4-y^2}dy$?

Published on 19 Nov 2022 - 12:08

score 81 · Answer 14 · 2022-11-23 21:35:20

81

Views

Integral involving a complete elliptic integral $\int_0^1 dt \frac{K(t)}{\sqrt{t\left(t+\frac{z}{1-z}\right)}}$

Published on 23 Nov 2022 - 21:35

score 60 · Answer 15 · 2026-03-26 17:14:24

60

Views

Reduction of the Degree of a Curve by a Substitution

Published on 26 Mar 2026 - 17:14

List Question

Is there a general relationship between definite integrals over functions involving the complete elliptic integral of the first kind and zeta values?

Euler's derivation of Lemniscate addition theorem

How to integrate Elliptic function with gaussian kernel

Simplifying indefinite integral (possibly in terms of elliptic integrals)

Find the integral for equation

Classification of integrals not expressible in elementary functions?

Periods and $\mathscr{P}(w)$ of the elliptic curve $y^2=4(x-1)(x-2)(x-3)$

Logarithmic Term in Elliptic Integral Expansion from Tonelli's Theorem

Are there tricks to calcualte the complete elliptic integral the third kind fast?

Show that the two elliptic integrals are equal

Jacobi's substitution for modular equations

Connection between modular equation and elliptic integral

What is the value of $\int_{\sqrt{3}}^{2}\sqrt{y^2-3}\sqrt{4-y^2}dy$?

Integral involving a complete elliptic integral $\int_0^1 dt \frac{K(t)}{\sqrt{t\left(t+\frac{z}{1-z}\right)}}$

Reduction of the Degree of a Curve by a Substitution

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