Question

Prime pattern found in the integral $\int_0^\pi \exp\left(\frac{\cos t}{8}\right)\cos\left(\frac{\sin t}{8}\right) \cos(nt )dt$

score 321 · Answer 1 · 2018-09-11 11:26:54

321

Views

Prime pattern found in the integral $\int_0^\pi \exp\left(\frac{\cos t}{8}\right)\cos\left(\frac{\sin t}{8}\right) \cos(nt )dt$

Published on 11 Sep 2018 - 11:26

score 104 · Answer 2 · 2018-09-11 23:22:00

104

Views

How can I represent following series as a formula?

Published on 11 Sep 2018 - 23:22

score 222 · Answer 3 · 2026-03-25 11:50:23

222

Views

Getting a closed form from $\sum_{i=1}^{n-1} \sum_{j=i+1}^{n} \sum_{k=1}^{j} 1$

Published on 25 Mar 2026 - 11:50

score 240 · Answer 4 · 2026-03-25 16:01:20

240

Views

Resolving nested dependent summation $ \sum_{i=1}^{n-1} \sum_{j=i+1}^{n} j $

Published on 25 Mar 2026 - 16:01

score 174 · Answer 5 · 2026-03-25 15:59:11

174

Views

Second-order nonlinear ODE involving cosine of the unknown function

Published on 25 Mar 2026 - 15:59

score 146 · Answer 6 · 2018-09-19 06:42:26

146

Views

From recurrence equation to closed proof by induction

Published on 19 Sep 2018 - 6:42

score 127 · Answer 7 · 2018-09-20 11:17:36

127

Views

A general expression for the summation of series with binomial coefficients : $\sum_{k=0}^{n}(-1)^k{{n}\choose{k}} \frac{1}{k+n}$

Published on 20 Sep 2018 - 11:17

score 1.6k · Answer 8 · 2018-09-21 09:53:34

1.6k

Views

How to derive the closed form of the summation $\sum_{i=1}^n d (i - 1)$?

Published on 21 Sep 2018 - 9:53

score 389 · Answer 9 · 2026-03-25 04:42:49

389

Views

How to compute the time complexity of a triple nested loop represented by $\sum_{i=1}^{2n} \sum_{j=1}^{n} \sum_{k=j}^{n} i-j$

Published on 25 Mar 2026 - 4:42

score 128 · Answer 10 · 2026-03-25 04:40:51

128

Views

What is the closed form of $\sum_{j=i}^{n} {j}$?

Published on 25 Mar 2026 - 4:40

score 332 · Answer 11 · 2018-09-26 08:56:27

332

Views

Find the value of $\int\limits_0^{+\infty} \frac{(\coth x-1)(x\coth x-1)}{x} dx$

Published on 26 Sep 2018 - 8:56

score 607 · Answer 12 · 2018-09-28 23:05:12

607

Views

Integral $\int_0^1 \ln\left(\frac{1-x}{1+x}\right)\ln\left(\frac{1-x^2}{1+x^2}\right)\frac{dx}{x}$

Published on 28 Sep 2018 - 23:05

score 102 · Answer 13 · 2018-09-29 12:05:01

102

Views

Show that $\int_0^1 {\sin \left( {\pi x} \right)} x^x \left( {1 - x} \right)^{1 - x} \mathrm dx = \frac{{\pi e}}{{24}}$

Published on 29 Sep 2018 - 12:05

score 842 · Answer 14 · 2026-03-25 01:18:42

842

Views

Show that $\int_0^{\infty}\frac{\operatorname{Li}_s(-x)}{x^{\alpha+1}}\mathrm dx=-\frac1{\alpha^s}\frac{\pi}{\sin(\pi \alpha)}$

Published on 25 Mar 2026 - 1:18

score 310 · Answer 15 · 2026-03-25 01:14:21

310

Views

Deriving the closed form of Gamma function using Euler-Chi function

Published on 25 Mar 2026 - 1:14

List Question

Prime pattern found in the integral $\int_0^\pi \exp\left(\frac{\cos t}{8}\right)\cos\left(\frac{\sin t}{8}\right) \cos(nt )dt$

How can I represent following series as a formula?

Getting a closed form from $\sum_{i=1}^{n-1} \sum_{j=i+1}^{n} \sum_{k=1}^{j} 1$

Resolving nested dependent summation $ \sum_{i=1}^{n-1} \sum_{j=i+1}^{n} j $

Second-order nonlinear ODE involving cosine of the unknown function

From recurrence equation to closed proof by induction

A general expression for the summation of series with binomial coefficients : $\sum_{k=0}^{n}(-1)^k{{n}\choose{k}} \frac{1}{k+n}$

How to derive the closed form of the summation $\sum_{i=1}^n d (i - 1)$?

How to compute the time complexity of a triple nested loop represented by $\sum_{i=1}^{2n} \sum_{j=1}^{n} \sum_{k=j}^{n} i-j$

What is the closed form of $\sum_{j=i}^{n} {j}$?

Find the value of $\int\limits_0^{+\infty} \frac{(\coth x-1)(x\coth x-1)}{x} dx$

Integral $\int_0^1 \ln\left(\frac{1-x}{1+x}\right)\ln\left(\frac{1-x^2}{1+x^2}\right)\frac{dx}{x}$

Show that $\int_0^1 {\sin \left( {\pi x} \right)} x^x \left( {1 - x} \right)^{1 - x} \mathrm dx = \frac{{\pi e}}{{24}}$

Show that $\int_0^{\infty}\frac{\operatorname{Li}_s(-x)}{x^{\alpha+1}}\mathrm dx=-\frac1{\alpha^s}\frac{\pi}{\sin(\pi \alpha)}$

Deriving the closed form of Gamma function using Euler-Chi function

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