Question

Closed form for $\prod\limits_{l=1}^\infty \cos\frac{x}{3^l}$

score 354 · Answer 1 · 2026-03-29 02:12:41

354

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Closed form for $\prod\limits_{l=1}^\infty \cos\frac{x}{3^l}$

Published on 29 Mar 2026 - 2:12

score 181 · Answer 2 · 2016-06-26 15:51:27

181

Views

A convergent series: $\sum_{n=0}^\infty 3^{n-1}\sin^3\left(\frac{\pi}{3^{n+1}}\right)$

Published on 26 Jun 2016 - 15:51

score 181 · Answer 3 · 2016-06-26 16:31:02

181

Views

Closed form of $\int_1^2\sqrt\frac{x^6+4x^4-2x^3+1}{x^4}\ \mathrm dx$

Published on 26 Jun 2016 - 16:31

score 1.6k · Answer 4 · 2016-06-27 05:24:12

1.6k

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How to integrate $\frac{dx}{(x-p)\sqrt {(x-p)(x-q)}} $?

Published on 27 Jun 2016 - 5:24

score 629 · Answer 5 · 2026-03-27 08:56:35

629

Views

Integral with Legendre polynomial: $\int_{-1}^{1}x^{n+2k}P_{n}(x)dx$

Published on 27 Mar 2026 - 8:56

score 72 · Answer 6 · 2016-06-27 16:12:17

72

Views

Maxima of $f(x)/e^x$ where $f(x)$ is an approximation of $e^x$ using Stirling's

Published on 27 Jun 2016 - 16:12

score 523 · Answer 7 · 2016-06-29 00:42:57

523

Views

Integral ${\large\int}_0^{\pi/2}\frac{x\,\log\tan x}{\sin x}\,dx$

Published on 29 Jun 2016 - 0:42

score 168 · Answer 8 · 2016-06-29 01:45:51

168

Views

Any hints on how to prove that $\ln{1\over 2\sin\left({90\over \pi}\right)}=\sum_{n=1}^{\infty}{(-1)^{n-1}B_{2n}\over 2n(2n)!}$?

Published on 29 Jun 2016 - 1:45

score 32 · Answer 9 · 2016-06-29 22:26:34

32

Views

"Solving" for a sequence given an (expected) expression for the summation

Published on 29 Jun 2016 - 22:26

score 1.8k · Answer 10 · 2016-06-30 03:20:57

1.8k

Views

Sum of nth powers of Fibonacci numbers

Published on 30 Jun 2016 - 3:20

score 1.2k · Answer 11 · 2016-06-30 19:29:28

1.2k

Views

How do I prove this $\int_{0}^{\infty}{e^{-x^n}-e^{-x^m}\over x\ln{x}}dx={\ln{\left(m\over n\right)}}?$

Published on 30 Jun 2016 - 19:29

score 268 · Answer 12 · 2016-07-02 14:21:14

268

Views

Evaluate $\int_0^\infty \frac{dx}{x^2+2ax+b}$

Published on 02 Jul 2016 - 14:21

score 174 · Answer 13 · 2026-03-30 15:04:10

174

Views

Evaluating $\int_ 1^2\frac{1}{x}dx$ with a Riemann Sum

Published on 30 Mar 2026 - 15:04

score 390 · Answer 14 · 2026-03-30 15:05:21

390

Views

Finding a Riemann sum for $f(x)=\frac{x^2}4+2$ over $[0,2]$.

Published on 30 Mar 2026 - 15:05

score 76 · Answer 15 · 2026-04-04 20:27:01

76

Views

Finding a line integral of $F(x,y) = (3x^2\cos y + 2\cos x, -x^3\sin y)$ along a given curve.

Published on 04 Apr 2026 - 20:27

List Question

Closed form for $\prod\limits_{l=1}^\infty \cos\frac{x}{3^l}$

A convergent series: $\sum_{n=0}^\infty 3^{n-1}\sin^3\left(\frac{\pi}{3^{n+1}}\right)$

Closed form of $\int_1^2\sqrt\frac{x^6+4x^4-2x^3+1}{x^4}\ \mathrm dx$

How to integrate $\frac{dx}{(x-p)\sqrt {(x-p)(x-q)}} $?

Integral with Legendre polynomial: $\int_{-1}^{1}x^{n+2k}P_{n}(x)dx$

Maxima of $f(x)/e^x$ where $f(x)$ is an approximation of $e^x$ using Stirling's

Integral ${\large\int}_0^{\pi/2}\frac{x\,\log\tan x}{\sin x}\,dx$

Any hints on how to prove that $\ln{1\over 2\sin\left({90\over \pi}\right)}=\sum_{n=1}^{\infty}{(-1)^{n-1}B_{2n}\over 2n(2n)!}$?

"Solving" for a sequence given an (expected) expression for the summation

Sum of nth powers of Fibonacci numbers

How do I prove this $\int_{0}^{\infty}{e^{-x^n}-e^{-x^m}\over x\ln{x}}dx={\ln{\left(m\over n\right)}}?$

Evaluate $\int_0^\infty \frac{dx}{x^2+2ax+b}$

Evaluating $\int_ 1^2\frac{1}{x}dx$ with a Riemann Sum

Finding a Riemann sum for $f(x)=\frac{x^2}4+2$ over $[0,2]$.

Finding a line integral of $F(x,y) = (3x^2\cos y + 2\cos x, -x^3\sin y)$ along a given curve.

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