Argon's user avatar
Argon's user avatar
Argon's user avatar
Argon
  • Member for 12 years
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48 votes

How to choose a proper contour for a contour integral?

43 votes
Accepted

How do you calculate the decimal expansion of an irrational number?

42 votes

Proving :$\arctan(1)+\arctan(2)+ \arctan(3)=\pi$

34 votes

"Simple" beautiful math proof

27 votes

Have there been efforts to introduce non Greek or Latin alphabets into mathematics?

25 votes

pronunciation of sinh x, cosh x, tanh x for short

25 votes

Is there any geometric way to characterize $e$?

25 votes
Accepted

How does $e^{\pi i}$ equal $-1$

23 votes
Accepted

How does $e^{i x}$ produce rotation around the imaginary unit circle?

23 votes

How to integrate $\int_{-\infty}^{+\infty} e^{-x^2}\cos x \, dx$

19 votes

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

18 votes
Accepted

"Sum equals integral" identities similar to $\int_0^1 \frac{dx}{x^x} = \sum_{n = 1}^{\infty} \frac{1}{n^n}$

17 votes

Cutting cake into 5 equal pieces

16 votes
Accepted

What is $\cot(\pi/2)$?

16 votes
Accepted

What do the $+,-$ mean in limit notation, like$\lim\limits_{t \to 0^+}$ and $\lim\limits_{t \to 0^-}$?

15 votes

Finding the sum of series; sum of squares

15 votes
Accepted

Show $\sum_{n=0}^\infty\frac{1}{a^2+n^2}=\frac{1+a\pi\coth a\pi}{2a^2}$

15 votes

Integral $\int_{-\infty}^\infty\frac{\Gamma(x)\,\sin(\pi x)}{\Gamma\left(x+a\right)}\,dx$

14 votes

Proving $\sqrt 3$ is irrational.

13 votes

Examples of mathematical induction

13 votes
Accepted

Why does $\cos (\pi\cos (\pi \cos (\log (20+\pi)))) \approx -1$

13 votes
Accepted

MIT Integration Bee $21$

12 votes
Accepted

Proving that $\int_0^\infty\frac{J_{2a}(2x)~J_{2b}(2x)}{x^{2n+1}}~dx~=~\frac12\cdot\frac{(a+b-n-1)!~(2n)!}{(n+a+b)!~(n+a-b)!~(n-a+b)!}$

12 votes
Accepted

Why do mathematicians care so much about zeta functions?

12 votes
Accepted

1 to the power i

11 votes
Accepted

What does ! mean in sequences?

11 votes
Accepted

Calculating derivative of $\operatorname{Log}(z)$

11 votes
Accepted

What is the meaning of $\exp(\,\cdot\,)$?

10 votes

The integral $\int_0^{\frac{\pi}{2}}\left(\frac{x}{\sin x}\right)^2\text{d}x$

10 votes
Accepted

Applications of Residue Theorem in complex analysis?

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