Mathlover

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2521

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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	3 hours ago

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169 Favorites

added views newest activity votes

148

378

votes

answers

kviews

Can I use my powers for good?

soft-question career-development

apr 11 at 0:40 MGA 80

votes

answers

kviews

Funny identities

big-list

apr 29 at 6:07 John Marty 1,117

votes

answers

kviews

Are non-circular manholes possible?

geometry

aug 1 at 15:15 Hans-Peter E. Kristiansen 445

votes

answers

kviews

Why can ALL quadratic equations be solved by the quadratic formula?

algebra-precalculus polynomials quadratics

jan 25 at 11:18 George Frank 131

votes

answers

kviews

How did Hermite calculate $e^{\pi\sqrt{163}}$ in 1859?

real-analysis math-history

jan 26 '12 at 3:52 J. M. 38.9k

votes

answers

kviews

Intuitive explanation of Cauchy's Integral Formula in Complex Analysis

intuition complex-analysis

apr 14 '11 at 5:18 Community♦ 1

votes

answers

536

views

Symmetry of function defined by integral

calculus

jan 4 at 19:20 Sasha 41.4k

votes

answer

493

views

A new continued fraction for Apéry's constant, $\zeta(3)$?

number-theory riemann-zeta continued-fractions

nov 25 at 12:24 J. M. 38.9k

votes

answers

983

views

Need a result of Euler that is simple enough for a child to understand

soft-question big-list education

feb 5 '12 at 6:04 Peter Tamaroff 26.1k

votes

answer

624

views

Is $1+x+\frac{x^2}2+\dots+\frac{x^n}{n!}$ irreducible?

abstract-algebra polynomials

apr 13 '12 at 5:40 Martin Sleziak 20.3k

votes

answers

kviews

Does $\zeta(3)$ have a connection with $\pi$?

sequences-and-series analysis pi riemann-zeta zeta-functions

apr 26 '12 at 21:10 Community♦ 1

votes

answers

kviews

Understanding Gödel's Incompleteness Theorem

logic incompleteness

nov 1 at 6:48 Holdsworth88 3,470

votes

answers

435

views

How to prove that $\int_0^1\left(\sum_{k=n}^\infty {x^k\over k}\right)^2\,dx = \int_0^1 2x^{n-1}\log\left(1+{1\over\sqrt{x}}\right)\,dx.$

integral

may 21 '12 at 5:04 Did 103k

votes

answers

632

views

On calculating $\displaystyle \int_0^1\ln(1-x^2)\;{dx}$ — where is the mistake?

analysis sequences-and-series integral power-series

mar 19 '11 at 19:46 joriki 92.8k

votes

answers

675

views

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

calculus real-analysis integral definite-integral improper-integrals

may 17 at 13:52 Cody 2,613

votes

answers

567

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 14.2k

votes

answers

994

views

Why is $\int_{0}^{\infty} \frac {\ln x}{1+x^2} \mathrm{d}x =0$?

calculus integral improper-integrals

jan 30 at 7:31 Mhenni Benghorbal 14.2k

votes

answers

520

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 14.2k

votes

answers

392

views

Asymptotic expression of an oscillatory integral

calculus asymptotics definite-integral

aug 30 at 0:48 Byron Schmuland 15.4k

votes

answers

360

views

Can you prove why consecutive diagonal intersection points show decreasing fractions inside a rectangle?

geometry analytic-geometry fractions

aug 23 at 19:12 Zach Stone 21

votes

answers

717

views

Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods?

real-analysis integral trigonometry

13h ago Chris's wise sister 11.5k

votes

answers

772

views

Original works of great mathematician Évariste Galois

number-theory reference-request algebraic-geometry galois-theory

aug 2 at 21:16 Philip Dabous 11

votes

answers

464

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Show $\int_{0}^{\frac{\pi}{2}}\frac{x^{2}}{x^{2}+\ln^{2}(2\cos(x))}dx=\frac{\pi}{8}\left(1-\gamma+\ln(2\pi)\right)$

calculus integral integration definite-integral

aug 4 at 23:41 sos440 14.4k

votes

answers

444

views

Approximation for $\pi$

math-history pi golden-ratio

may 20 '12 at 19:00 Robert Israel 86.5k

votes

answers

357

views

An interesting sum to infinity

calculus real-analysis sequences-and-series limit special-functions

feb 8 at 19:04 Chris's wise sister 11.5k

votes

answers

200

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 9,190

votes

answers

280

views

Summation using residues

calculus complex-analysis complex-integration

may 10 at 9:37 Cody 2,613

votes

answer

731

views

Intuition behind looking at permutations of the roots in Galois theory

intuition galois-theory

sep 16 '11 at 18:24 Arturo Magidin 158k

votes

answer

465

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Compute $ I_{n}=\int_{-\infty}^\infty \frac{1-\cos x \cos 2x \cdots \cos nx}{x^2}\,dx$

calculus real-analysis integral

aug 7 at 14:18 Chris's wise sister 11.5k

votes

answers

729

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Possibility to simplify $\sum\limits_{k = - \infty }^\infty {\frac{{{{\left( { - 1} \right)}^k}}}{{a + k}} = \frac{\pi }{{\sin \pi a}}} $

calculus sequences-and-series trigonometry special-functions

oct 28 at 3:57 Argon 9,276