Mathlover

2,900 reputation

2521

bio	website
	location
	age
visits	member for	1 year, 4 months
	seen	1 hour ago
stats	profile views	333

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.

	2,900 reputation	bio	website		visits	member for	1 year, 4 months
2521 badges		location			seen	1 hour ago

summary answers questions tags badges favorites bounties reputation activity

165 Favorites

added views newest activity votes

votes

answers

681

views

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

calculus integral

14h ago kee wen 1

votes

answers

669

views

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

may 17 at 13:52 Cody 2,613

votes

answers

561

views

Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$

real-analysis sequences-and-series

may 17 at 6:54 Mhenni Benghorbal 14k

votes

answers

352

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

answers

276

views

Summation using residues

calculus complex-analysis complex-integration

may 10 at 9:37 Cody 2,613

votes

answers

kviews

How do we prove $\cos(\pi/5) - \cos(2\pi/5) = 0.5$ ?.

trigonometry

may 9 at 8:00 Stefan Hansen 8,518

votes

answer

283

views

Formula for Legendre polynomials by use of Cauchy's Integral Formula (From _Visual Complex Analysis_)

complex-analysis polynomials

may 3 at 10:45 chisom 1

votes

answers

kviews

Funny identities

big-list

apr 29 at 6:07 John Marty 974

votes

answers

305

views

Calculating $\frac{\partial^{1/2}}{\partial x^{1/2}}\left( e^{-\alpha x^2 + \beta x} \right) $

fractional-calculus

apr 25 at 12:59 Mhenni Benghorbal 14k

votes

answer

187

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 2,247

votes

answers

296

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. 38.9k

votes

answer

126

views

Show that Bessel function $J_n(x)$ satisfies Bessel's differential equation.

differential-equations special-functions

apr 12 at 13:00 J. M. 38.9k

votes

answers

kviews

What is the real life use of hyperbola?

conic-sections applications

apr 11 at 21:24 nneonneo 115

148

376

votes

answers

kviews

Can I use my powers for good?

soft-question career-development

apr 11 at 0:40 MGA 75

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. 38.9k

votes

answer

135

views

closed-form expression for roots of a polynomial

polynomials galois-theory roots

apr 6 at 17:52 J. M. 38.9k

votes

answers

129

views

Series $\sum_{k=1}^\infty \left(\frac{1}{k}-\frac{1}{k+z} \right)$

sequences-and-series analysis

mar 31 at 21:30 Raymond Manzoni 15.3k

votes

answers

519

views

How to evaluate $I=\displaystyle\int_0^{\pi/2}x^2\ln(\sin x)\ln(\cos x)dx$

integral

mar 31 at 13:27 Mhenni Benghorbal 14k

vote

answers

107

views

Solution to a second order Riccati equation

differential-equations

mar 27 at 15:42 Mike MacNeil 1

votes

answers

249

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

120

views

A question about an equilateral triangle

geometry

mar 15 at 16:47 lab bhattacharjee 28.5k

votes

answers

110

views

Integral of irrational function

calculus integral

mar 13 at 18:01 Thomas Andrews 29.6k

vote

answer

208

views

Polynomial of polynomials (from Brilliant.org)

polynomials contest-math

mar 11 at 16:54 robjohn♦ 59.3k

votes

answers

109

views

Evaluate $\frac{1}{2\pi}\int _{-\pi}^\pi \frac{e^{-i\varphi}}{1-k\cos (\varphi)} \, \mathrm{d}\varphi$

integral

mar 9 at 19:27 vonbrand 6,568

votes

answer

133

views

Find the value $\sum_{m=1}^{\infty}{\frac{e^{-a m^2}}{m^2}}$

calculus real-analysis sequences-and-series analysis

mar 8 at 7:35 Raymond Manzoni 15.3k

votes

answers

336

views

Is there a Definite Integral Representation for $n^n$?

number-theory definite-integral exponentiation

mar 5 at 12:29 Community♦ 1

votes

answers

122

views

Unusual evaluation of $\sum \frac{1}{n^2}$

homework complex-analysis

mar 4 at 8:10 Jonathan 3,889

votes

answer

109

views

Prove that $\int_0^{\pi/2} \cos^{p+q-2}(\theta) \cos((p-q)\theta)d\theta = \frac{\pi}{(p+q-1)2^{p+q-1}B(p,q)}$

complex-analysis special-functions definite-integral

mar 3 at 12:44 Random Variable 1,617

votes

answers

154

views

Need some hint or technique for this integral

calculus real-analysis sequences-and-series integral

mar 2 at 14:12 Sasha 41.4k

votes

answers

199

views

How to prove summation, multiplication, subtraction of two roots of $1+x+\frac{x^2}{2!}+\cdots+\frac{x^p}{p!}=0$ aren't rationals?

homework polynomials algebraic-number-theory galois-theory

mar 2 at 10:13 YACP 9,015