user avatar
user avatar
user avatar
mnsh
  • Member for 9 years, 4 months
  • Last seen this week
  • Damascus, Syria
44 votes
3 answers
1k views

Is there a function with the property$ f(n)=f^{(n)}(a)$

28 votes
5 answers
8k views

Find closed form for $1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 10, \ldots$

19 votes
4 answers
2k views

Finding the fraction $\frac{a^5+b^5+c^5+d^5}{a^6+b^6+c^6+d^6}$ when knowing the sums $a+b+c+d$ to $a^4+b^4+c^4+d^4$

17 votes
3 answers
3k views

integral of $\int \limits_{0}^{\infty}\frac {\sin (x^n)} {x^n}dx$

13 votes
2 answers
2k views

closed form of $\int_{0}^{2\pi}\frac{dx}{(a^2\cos^2x+b^2\sin^2x)^n}$

13 votes
8 answers
2k views

show that $\int_{0}^{\infty} \frac {\sin^3(x)}{x^3}dx=\frac{3\pi}{8}$

12 votes
1 answer
2k views

How to prove that $\frac{\sin \pi x}{\pi x}=\prod_{n=1}^{\infty}(1-\frac{x^2}{n^2})$ [duplicate]

12 votes
1 answer
425 views

Closed form for $I=\int_{0}^{\infty}\frac{x^n}{x^2+u^2}\tanh(x) \, dx$

11 votes
3 answers
4k views

show that $\int_{0}^{\infty } \frac {\cos (ax) -\cos (bx)} {x^2}dx=\pi \frac {b-a} {2}$

9 votes
4 answers
1k views

Find the limit without use of L'Hôpital or Taylor series: $\lim \limits_{x\rightarrow 0} \left(\frac{1}{x^2}-\frac{1}{\sin^2 x}\right)$

9 votes
6 answers
3k views

Evaluate $ \lim_{x \to 0} \frac{x^2}{x+\sin (\frac 1 x)} $

9 votes
2 answers
221 views

closed form for $I(n)=\int_0^1\left ( \frac{\pi}{4}-\arctan x \right )^n\frac{1+x}{1-x}\frac{dx}{1+x^2}$

8 votes
2 answers
187 views

show that $\int_0^{\infty}\sin(u\cosh x)\sin(u\sinh x)\frac{dx}{\sinh x}=\frac{\pi }{2}\sin u$

7 votes
5 answers
2k views

show that $\int_{0}^{\infty } \frac{\sin (ax)}{x(x^2+b^2)^2}dx=\frac{\pi}{2b^4}(1-\frac{e^{-ab}(ab+2)}{2})$

7 votes
1 answer
3k views

what is the best book to study contour integration?

7 votes
4 answers
286 views

show that $\lim_{n \to \infty} n\int_0^1 e^{-tn}(\frac{\sinh t}{t})^n \, dt=1$

7 votes
2 answers
94 views

show that $\sum_{n=1}^{\infty}\frac{1}{n+1}\sum_{k=0}^{n}(-1)^{k+1}\binom{n}{k}\log(k+1)=1$ [closed]

6 votes
1 answer
131 views

closed form for $\int_{0}^{\infty}\frac{ \beta(a+ix,a-ix)}{\beta(b+ix,b-ix)}\frac{dx}{(b^2+x^2)}$

6 votes
3 answers
175 views

What is the domain of $x^x$ when $ x<0$

6 votes
1 answer
157 views

show that $e=(\frac{2}{1})^{\frac{1}{1}}(\frac{4}{3})^{\frac{1}{2}}(\frac{6\cdot8}{5\cdot7})^{\frac{1}{4}}...$

6 votes
1 answer
297 views

Is there closed form for $\int_0^{\pi/4}\exp(-\sum_{n=1}^{\infty}\frac{\tan^{2n}x}{n+a})\ dx$?

6 votes
3 answers
592 views

Check whether $36^{36}+41^{41}$ a multiple of $77$

6 votes
8 answers
1k views

show that $\int_{0}^{\pi/2}\ln(\tan x)dx=0$

6 votes
5 answers
266 views

show that $\int_{-\infty}^{+\infty} \frac{dx}{(x^2+1)^{n+1}}=\frac {(2n)!\pi}{2^{2n}(n!)^2}$

6 votes
4 answers
3k views

show that $\int_{0}^{\infty}\frac{x\cos ax}{\sinh x}dx=\frac{\pi^2}{4} \operatorname{sech}^2 \left(\frac{a\pi}{2}\right) $

5 votes
1 answer
322 views

Where is the mistake in this argument that $(\sqrt8)^{\sqrt 7} >(\sqrt7)^{\sqrt 8}$?

5 votes
1 answer
596 views

The series of $\frac{1}{\cosh(z)}$

5 votes
4 answers
424 views

Show that $\int \limits_{0}^{\infty}\frac{x}{\sinh ax}dx=\left(\frac{\pi}{2a}\right)^2$

5 votes
1 answer
111 views

using complex or real analysis solve $\int_{0}^{\pi/2}\frac{x^m}{\sin x}dx$

4 votes
0 answers
281 views

show that $\int_{0}^{\infty}e^{-x}\ln(x)dx=-\gamma=\Gamma'(1) $ [duplicate]