Question

On the trigonometric roots of a cubic

score 719 · Answer 1 · 2026-03-27 16:39:50

719

Views

On the trigonometric roots of a cubic

Published on 27 Mar 2026 - 16:39

score 113 · Answer 2 · 2026-03-28 00:05:53

113

Views

On the trigonometric roots of some quintics

Published on 28 Mar 2026 - 0:05

score 85 · Answer 3 · 2026-03-26 16:57:31

85

Views

Are these two expressions equivalent? Checking by hand or Mathematica

Published on 26 Mar 2026 - 16:57

score 90 · Answer 4 · 2016-11-23 11:20:35

90

Views

What is the exact closed form of $2^1\cdot1^{2}+2^2\cdot2^{2}+2^3\cdot3^{2}+\cdots+2^n\cdot n^{2}$?

Published on 23 Nov 2016 - 11:20

score 1.7k · Answer 5 · 2016-11-25 11:20:42

1.7k

Views

Proof $\int_{-\infty}^\infty\frac{dx}{\left(e^x+e^{-x}+e^{ix\sqrt{3}}\right)^2}=\frac{1}{3}$

Published on 25 Nov 2016 - 11:20

score 432 · Answer 6 · 2026-03-25 16:03:45

432

Views

Conjecture for the value of $\int_0^1 \frac{1}{1+x^{p}}dx$

Published on 25 Mar 2026 - 16:03

score 903 · Answer 7 · 2026-03-29 10:49:10

903

Views

On the integral $\int_0^\infty \eta^2(i x) \,dx = \ln(1+\sqrt{3}+\sqrt{3+2 \sqrt{3}})$ and its cousins

Published on 29 Mar 2026 - 10:49

score 74 · Answer 8 · 2016-11-27 09:04:00

74

Views

Z transform (transform function and impulse response)

Published on 27 Nov 2016 - 9:04

score 430 · Answer 9 · 2016-11-28 10:20:34

430

Views

When the graph of a function on compact topological space is closed, compact, connected

Published on 28 Nov 2016 - 10:20

score 63 · Answer 10 · 2016-11-28 20:44:30

63

Views

Finding a closed form of this series: $\sum_{n = 1}^{\infty} {n-\sqrt{n^2+1}\over\sqrt{n(n+1)}}$

Published on 28 Nov 2016 - 20:44

score 160 · Answer 11 · 2026-03-28 07:38:34

160

Views

How to show that $\int_0^{\pi/2}\int_0^{\pi/2}\left(\frac{\sin\phi}{\sin\theta}\right)^{1/2}\,d\theta\,d\phi=\pi$?

Published on 28 Mar 2026 - 7:38

score 105 · Answer 12 · 2016-11-28 21:37:09

105

Views

Convergence and evaluation of $\sum_{n=1}^{\infty}\ln {(2n+1)n \over (n+1)(2n-1)}$

Published on 28 Nov 2016 - 21:37

score 310 · Answer 13 · 2026-03-28 13:42:06

310

Views

Is there a closed-form for $\frac{d^ny}{dx^n}$?

Published on 28 Mar 2026 - 13:42

score 804 · Answer 14 · 2026-03-25 06:06:48

804

Views

On Reshetnikov's integral $\int_0^1\frac{dx}{\sqrt[3]x\ \sqrt[6]{1-x}\ \sqrt{1-x\,\alpha^2}}=\frac{1}{N}\,\frac{2\pi}{\sqrt{3}\,|\alpha|}$

Published on 25 Mar 2026 - 6:06

score 1.1k · Answer 15 · 2026-03-25 07:45:36

1.1k

Views

On the integral $\int_0^1\frac{dx}{\sqrt[4]x\ \sqrt{1-x}\ \sqrt[4]{1-x\,\gamma^2}}=\frac{1}{N}\,\frac{2\pi}{\sqrt{2\gamma}}$

Published on 25 Mar 2026 - 7:45

List Question

On the trigonometric roots of a cubic

On the trigonometric roots of some quintics

Are these two expressions equivalent? Checking by hand or Mathematica

What is the exact closed form of $2^1\cdot1^{2}+2^2\cdot2^{2}+2^3\cdot3^{2}+\cdots+2^n\cdot n^{2}$?

Proof $\int_{-\infty}^\infty\frac{dx}{\left(e^x+e^{-x}+e^{ix\sqrt{3}}\right)^2}=\frac{1}{3}$

Conjecture for the value of $\int_0^1 \frac{1}{1+x^{p}}dx$

On the integral $\int_0^\infty \eta^2(i x) \,dx = \ln(1+\sqrt{3}+\sqrt{3+2 \sqrt{3}})$ and its cousins

Z transform (transform function and impulse response)

When the graph of a function on compact topological space is closed, compact, connected

Finding a closed form of this series: $\sum_{n = 1}^{\infty} {n-\sqrt{n^2+1}\over\sqrt{n(n+1)}}$

How to show that $\int_0^{\pi/2}\int_0^{\pi/2}\left(\frac{\sin\phi}{\sin\theta}\right)^{1/2}\,d\theta\,d\phi=\pi$?

Convergence and evaluation of $\sum_{n=1}^{\infty}\ln {(2n+1)n \over (n+1)(2n-1)}$

Is there a closed-form for $\frac{d^ny}{dx^n}$?

On Reshetnikov's integral $\int_0^1\frac{dx}{\sqrt[3]x\ \sqrt[6]{1-x}\ \sqrt{1-x\,\alpha^2}}=\frac{1}{N}\,\frac{2\pi}{\sqrt{3}\,|\alpha|}$

On the integral $\int_0^1\frac{dx}{\sqrt[4]x\ \sqrt{1-x}\ \sqrt[4]{1-x\,\gamma^2}}=\frac{1}{N}\,\frac{2\pi}{\sqrt{2\gamma}}$

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