Question

Proving $\displaystyle\lim_{m\rightarrow \infty}\sqrt {2m+1}\int_{0}^{1}\frac{t^{(2m+1)n}}{\sqrt {1-t^{2n}}}\,dt\ $ exists and is positive

score 88 · Answer 1 · 2020-02-12 04:59:33

88

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Proving $\displaystyle\lim_{m\rightarrow \infty}\sqrt {2m+1}\int_{0}^{1}\frac{t^{(2m+1)n}}{\sqrt {1-t^{2n}}}\,dt\ $ exists and is positive

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score 328 · Answer 2 · 2026-03-25 09:25:34

328

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Umemura's Theorem on Solving any Algebraic Polynomial Equation

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score 394 · Answer 3 · 2020-02-16 12:00:07

394

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score 41 · Answer 4 · 2020-02-27 00:06:21

41

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score 110 · Answer 5 · 2020-02-27 07:51:48

110

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score 56 · Answer 6 · 2020-03-04 15:35:05

56

Views

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score 102 · Answer 7 · 2020-03-13 14:05:36

102

Views

Calculate $\int_0^a \frac{dx}{\sqrt{x^4+x^2+1}}$ in terms of $\int_0^a \frac{dx}{\sqrt{x^4+1}}$

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score 34 · Answer 8 · 2020-03-25 23:42:44

34

Views

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score 128 · Answer 9 · 2020-03-26 19:32:48

128

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score 75 · Answer 10 · 2020-03-27 16:25:53

75

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209

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score 317 · Answer 12 · 2020-04-03 19:23:28

317

Views

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score 79 · Answer 13 · 2020-04-06 09:04:35

79

Views

How can i prove that the elliptic intergal is equal to this double sum? $\Pi(n|m)=\int _0^{\frac{\pi}{2}}\frac{1}{(1-n\sin^2t)\sqrt{1-m\sin^2t}}dt=..$

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score 30 · Answer 14 · 2020-04-06 15:44:24

30

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score 268 · Answer 15 · 2020-04-10 07:42:38

268

Views

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List Question

Proving $\displaystyle\lim_{m\rightarrow \infty}\sqrt {2m+1}\int_{0}^{1}\frac{t^{(2m+1)n}}{\sqrt {1-t^{2n}}}\,dt\ $ exists and is positive

Umemura's Theorem on Solving any Algebraic Polynomial Equation

Relation between different types of elliptic functions

How to solve this incomplete elliptic equation in Matlab? Thank you!

Integral of $\sqrt{c-\cos(x)}$ where c is a constant

Does a bijection $\phi$ which is not a morphism between two projective plane curves $C$ and $D$ induces an isomorphism $\phi^{*}$ on function fields?

Calculate $\int_0^a \frac{dx}{\sqrt{x^4+x^2+1}}$ in terms of $\int_0^a \frac{dx}{\sqrt{x^4+1}}$

The function $K(k)E(k)-k'^2K^2(k)$ is differentiable strictly increasing?

Complete elliptic integrals

cosine Elliptic Integral with an indeterminate answer

Integral involving elliptic integral functions

series expansion of elliptic integral of the third kind

How can i prove that the elliptic intergal is equal to this double sum? $\Pi(n|m)=\int _0^{\frac{\pi}{2}}\frac{1}{(1-n\sin^2t)\sqrt{1-m\sin^2t}}dt=..$

Equal uncomputable integrals

Understanding asymptotic expansion of elliptic integral

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