User Potato - Mathematics Stack Exchange

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32

60

votes

6

answers

1

kviews

Contest problem about convergent series

nov 21 at 20:48 robjohn♦ 60.1k

25

53

votes

3

answers

2

kviews

Is there an integral that proves $\pi > 333/106$?

calculus real-analysis integral approximation pi

feb 25 at 15:59 Michael Hardy 48.4k

32

49

votes

16

answers

8

kviews

If $AB = I$ then $BA = I$

linear-algebra matrices

may 1 at 22:19 mezhang 1,433

15

41

votes

3

answers

648

views

Proof of $\frac{1}{e^{\pi}+1}+\frac{3}{e^{3\pi}+1}+\frac{5}{e^{5\pi}+1}+\ldots=\frac{1}{24}$

sequences-and-series reference-request fourier-series modular-forms elliptic-functions

may 14 at 3:00 Marko Riedel 1,939

16

37

votes

2

answers

538

views

Looking for a function such that…

functional-analysis functions functional-equations

oct 15 at 21:23 asperanz 161

14

31

votes

5

answers

904

views

How to prove this identity $\pi=\sum\limits_{k=-\infty}^{\infty}\left(\frac{\sin(k)}{k}\right)^{2}\;$?

sequences-and-series trigonometry pi

may 7 at 15:34 robjohn♦ 60.1k

13

30

votes

4

answers

820

views

Rain droplets falling on a table

calculus probability integral probability-theory integration

aug 8 at 0:47 joriki 92.8k

19

30

votes

3

answers

816

views

Does the series $ \sum\limits_{n=1}^{\infty} \frac{1}{n^{1 + |\sin(n)|}} $ converge or diverge?

real-analysis sequences-and-series convergence diophantine-approximation

jan 4 at 18:23 Byron Schmuland 15.4k

16

28

votes

2

answers

2

kviews

The square roots of the primes are linearly independent over the field of rationals

abstract-algebra prime-numbers field-theory

oct 7 at 23:05 Community♦ 1

9

28

votes

5

answers

1

kviews

Continuity of the roots of a polynomial in terms of its coefficients

analysis polynomials field-theory roots

sep 10 '11 at 9:48 Georges Elencwajg 45k

8

22

votes

3

answers

1

kviews

$\pi_{1}({\mathbb R}^{2} - {\mathbb Q}^{2})$ is uncountable

algebraic-topology

sep 10 '11 at 14:52 spencer 11

14

21

votes

3

answers

361

views

Intuition for the Importance of Modular Forms

number-theory intuition modular-forms

apr 10 at 7:23 Rohit Chatterjee 1

8

20

votes

7

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

5

20

votes

2

answers

406

views

Distance from $x^n$ to lesser polynomials

real-analysis polynomials approximation-theory

jan 12 '12 at 1:32 robjohn♦ 60.1k

7

19

votes

2

answers

481

views

$\int_{0}^{\infty} \frac{\cos x - e^{-x^2}}{x} \ dx$ Evaluate Integral

calculus real-analysis integral integration improper-integrals

mar 1 at 22:27 Arjang 2,447

6

18

votes

3

answers

451

views

Evaluate:: $ 2 \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n+1}\left( 1 + \frac12 +\cdots + \frac 1n\right) $

real-analysis sequences-and-series

feb 6 at 17:58 user17762 76.6k

8

18

votes

1

answer

425

views

How did Ramanujan get this result?

calculus

jun 20 '12 at 13:21 Cocopuffs 5,214

6

17

votes

3

answers

384

views

Prove $\int_0^1 \frac{t^2-1}{(t^2+1)\ln t}dt = 2\log\left( \frac{2\Gamma \left( \frac{5}{4}\right)}{\Gamma\left( \frac{3}{4}\right)}\right)$

calculus integral integration definite-integral

jan 24 at 0:21 robjohn♦ 60.1k

6

16

votes

3

answers

377

views

The limit of $\frac{n+\sqrt{n}+\cdots+\sqrt[n]{n}}{n}$

limit

jun 27 '12 at 2:53 Zarrax 19.7k

8

16

votes

2

answers

420

views

Inequality on the side lengths of a triangle: $\left| \frac{a}{b} + \frac{b}{c} + \frac{c}{a} - \frac{a}{c} - \frac{b}{a} - \frac{c}{b} \right| < 1$.

geometry inequality contest-math

jan 25 at 6:31 Haskell Curry 11.1k

6

15

votes

2

answers

362

views

Compute: $\lim_{n\to\infty}\frac{{\left(1^1 \cdot 2^2 \cdot3^3\cdots n^n\right)}^\frac{1}{n^2}}{\sqrt{n}} $

calculus real-analysis limit

feb 8 at 19:02 Chris's wise sister 11.5k

5

14

votes

3

answers

295

views

Small exercise?

homework analysis

mar 6 at 20:21 Robert Haraway 965

5

14

votes

1

answer

197

views

Galois group for $x^6-7x^2+7$

abstract-algebra

mar 18 at 22:16 Steve D 5,270

7

13

votes

2

answers

384

views

Prove $\int_0^\infty \frac{\ln(\tan^2 (ax))}{1+x^2}dx = \pi\ln(\tanh(a))$

calculus integral integration improper-integrals

apr 3 at 11:51 DonAntonio 47.2k

6

13

votes

4

answers

1

kviews

Convergence of the sequence $\sqrt{1+2\sqrt{1}},\sqrt{1+2\sqrt{1+3\sqrt{1}}},\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1}}}},\cdots$

sequences-and-series limit

dec 15 at 18:15 Abhishek 1

3

12

votes

4

answers

2

kviews

Prove: $\int_{0}^{\infty} \sin (x^2) dx$ converges.

calculus integral improper-integrals

feb 3 '12 at 1:00 ncmathsadist 17.2k

3

11

votes

1

answer

277

views

How do experts mentally classify indefinite integrals?

soft-question indefinite-integral

feb 10 '12 at 18:34 Community♦ 1

2

11

votes

2

answers

520

views

Continuity of analytic function implies convergence of power series?

complex-analysis

jan 27 at 19:06 David Speyer 18.7k

6

11

votes

1

answer

289

views

Compute $\sum_{k=1}^{\infty}e^{-\pi k^2}\left(\pi k^2-\frac{1}{4}\right)$

calculus real-analysis sequences-and-series limit

feb 9 at 0:50 Marko Riedel 1,939

3

11

votes

2

answers

168

views

Evaluating $ \int^{\infty}_{-\infty}\sin\left({\pi}^{4}x^{2}+\frac{1}{x^2}\right) dx$

integration

may 21 at 3:00 Asaf Karagila 91.8k

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