Mathlover

2,930 reputation

2521

bio	website
	location
	age
visits	member for	1 year, 4 months
	seen	4 hours ago
stats	profile views	340

I am an engineer who is in love with math and lifelong math student. I love to learn new things in mathematics for self-satisfaction. My idols are Gauss , Euler , Ramanujan because they were in love with math as I feel.

	2,930 reputation	bio	website		visits	member for	1 year, 4 months
2521 badges		location			seen	4 hours ago

summary answers questions tags badges favorites bounties reputation activity

169 Favorites

added views newest activity votes

votes

answers

394

views

The function $f(x) = \int_0^\infty \frac{x^t}{\Gamma(t+1)} \, dt$

jun 17 '12 at 8:44 oen 7,497

votes

answers

381

views

What is $i$ exponentiated to itself $i$ times?

complex-numbers tetration

jan 17 at 20:13 Alraxite 419

votes

answers

344

views

Can this integral $\int_0^{2\pi} \frac{d\theta}{(a^2 \cos^2 \theta +b^2\sin^2\theta)^{3/2}}$ be written in the form of a elliptic integral

integral special-functions elliptic-integrals

jul 13 at 14:47 J. M. 39k

votes

answers

286

views

For which $n$ is $ \int \limits_0^{2\pi} \prod \limits_{k=1}^n \cos(k x)\,dx $ non-zero?

calculus real-analysis integral integration

feb 15 at 21:50 Alexander Gruber♦ 15.3k

votes

answers

806

views

Evaluating $\int\limits_0^\infty \! \frac{x^{1/n}}{1+x^2} \ \mathrm{d}x$

calculus complex-analysis integral integration improper-integrals

aug 6 at 23:26 Rajesh K Singh 1,009

votes

answers

kviews

What is the real life use of hyperbola?

conic-sections applications

apr 11 at 21:24 nneonneo 115

votes

answers

304

views

How to prove $\sum\limits_{k=0}^n{n \choose k}(k-1)^k(n-k+1)^{n-k-1}= n^n$?

combinatorics discrete-mathematics binomial-coefficients

apr 15 at 10:19 J. M. 39k

votes

answer

190

views

Interesting Integral $\int_{-\infty}^{\infty}\frac{e^{i nx}}{\Gamma(\alpha+x) \Gamma(\beta -x)}dx$

integral special-functions improper-integrals gamma-function

apr 18 at 1:18 daniel 2,252

votes

answers

kviews

Methods to see if a polynomial is irreducible

abstract-algebra polynomials

may 4 '11 at 8:10 Bruno Stonek 3,148

votes

answers

kviews

How Can One Prove $\cos(\pi/7) + \cos(3 \pi/7) + \cos(5 \pi/7) = 1/2$

trigonometry proof-strategy popular-math

sep 19 at 19:37 Chris's wise sister 11.5k

votes

answers

252

views

How to prove that $\frac{d^n}{dx^n}(x^2-1)^n=0$ has $n$ real roots?

differential-equations

jan 31 at 1:29 robjohn♦ 60.1k

votes

answers

441

views

Careers in Math

soft-question self-learning career-development

nov 17 at 3:43 amWhy 55.4k

votes

answer

343

views

Behaviour of the series $\exp_p(x)=\sum_{k=0}^{\infty}\frac{x^k}{(k!)^p}$ depending on $p\approx 2$?

sequences-and-series special-functions

apr 28 '11 at 9:39 J. M. 39k

votes

answers

359

views

$\int_{0}^{\infty}\frac{\sin^{2n+1}(x)}{x} \mathrm {d}x$ Evaluate Integral

calculus integral trigonometry integration improper-integrals

may 11 at 17:19 Lia Denisse 106

votes

answer

217

views

What is the binomial sum $\sum_{n=1}^\infty \frac{1}{n^5\,\binom {2n}n}$ in terms of zeta functions?

special-functions binomial-coefficients analytic-number-theory riemann-zeta zeta-functions

may 14 '12 at 18:32 Tito Piezas III 2,680

votes

answers

975

views

What philosophical consequence of Goedel's incompleteness theorems?

logic computability philosophy incompleteness

apr 14 '12 at 20:04 Iasafro Maesman 955

votes

answer

338

views

Evaluating $\int_0^1 \log \log \left(\frac{1}{x}\right) \frac{dx}{1+x^2}$

calculus integral

apr 14 '12 at 9:29 J. M. 39k

votes

answers

250

views

Closed form for $\sum_{k=0}^{n} k\binom{n}{k}\log\binom{n}{k}$

sequences-and-series asymptotics binomial-coefficients

mar 25 at 18:29 Byron Schmuland 15.4k

votes

answers

382

views

Evaluating $\int_a^b \arccos\left(x\,/\sqrt{(a+b)x-ab\,}\,\right)\,\mathrm {d}x$ assuming $0<a<b$

integral

mar 19 '12 at 17:42 Byron Schmuland 15.4k

votes

answers

402

views

Showing $f'(x) = f(x)$ implies an exponential function

homework derivatives

mar 20 '12 at 0:50 Mathlover 2,930

votes

answers

524

views

Solve the integral $S_k = (-1)^k \int_0^1 (\log(\sin \pi x))^k dx$

calculus integral

apr 7 at 16:13 J. M. 39k

votes

answers

698

views

Is there really no way to integrate $e^{-x^2}$?

calculus integral

may 20 at 16:37 kee wen 1

votes

answers

406

views

Complex towers: $i^{i^{i^{…}}}$

complex-analysis tetration

sep 17 at 10:02 Community♦ 1

votes

answers

709

views

Proof of $\frac{d}{dx}e^x = e^x$

calculus limit

sep 16 at 18:19 voithos 165

votes

answers

209

views

Calculation of a strange series

sequences-and-series

sep 11 at 19:14 Sasha 41.4k

votes

answer

359

views

How to evaluate $\int_{0}^{1}{\frac{{{\ln }^{2}}\left( 1-x \right){{\ln }^{2}}\left( 1+x \right)}{1+x}dx}$

calculus sequences-and-series integral integration summation

dec 28 at 20:13 oen 7,497

votes

answers

299

views

Triangle problem

homework geometry

oct 14 at 9:05 Christian Blatter 32.7k

votes

answer

253

views

Evaluating $\int_{0}^{\infty}(\ln \tan^2 bx)/(a^2+x^2)\ dx$

integral

jul 11 at 0:29 Community♦ 1

votes

answers

111

views

infinite series involving harmonic numbers and zeta

sequences-and-series

jun 20 '12 at 15:35 Cody 2,613

votes

answers

162

views

Solving for unknown functions

calculus integral-equations

jul 29 at 12:28 Raymond Manzoni 15.4k