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Raymond Manzoni's user avatar
Raymond Manzoni's user avatar
Raymond Manzoni's user avatar
Raymond Manzoni
  • Member for 12 years, 6 months
  • Last seen this week
364 votes

Examples of patterns that eventually fail

266 votes

How to check if a point is inside a rectangle?

196 votes
Accepted

How to determine with certainty that a function has no elementary antiderivative?

141 votes

Help find hard integrals that evaluate to $59$?

89 votes

Demystify integration of $\int \frac{1}{x} \mathrm dx$

72 votes
Accepted

Getting the sequence $\{1, 0, -1, 0, 1, 0, -1, 0, \ldots\}$ without trig?

71 votes

How to calculate the area of a 3D triangle?

69 votes
Accepted

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

60 votes
Accepted

Why is there no "remainder" in multiplication

56 votes

Conjecture $_2F_1\left(\frac14,\frac34;\,\frac23;\,\frac13\right)=\frac1{\sqrt{\sqrt{\frac4{\sqrt{2-\sqrt[3]4}}+\sqrt[3]{4}+4}-\sqrt{2-\sqrt[3]4}-2}}$

43 votes

Why do we need to learn integration techniques?

40 votes
Accepted

How to figure out the log of a number without a calculator?

38 votes

Two Representations of the Prime Counting Function

37 votes
Accepted

Formula for $\zeta(3)$ -verification

36 votes
Accepted

Infinite Series $\sum_{n=1}^\infty\frac{H_n}{n^22^n}$

33 votes
Accepted

Real and imaginary part of Gamma function

31 votes
Accepted

what is the relation between quaternions and imaginary numbers?

29 votes
Accepted

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

29 votes
Accepted

Approximation of $e$ using $\pi$ and $\phi$?

28 votes
Accepted

Zeta function zeros and analytic continuation

26 votes
Accepted

Is there any proof that the Riemann Zeta function is not elementary?

25 votes

Integrals of the form ${\large\int}_0^\infty\operatorname{arccot}(x)\cdot\operatorname{arccot}(a\,x)\cdot\operatorname{arccot}(b\,x)\ dx$

24 votes

How to expand $\tan x$ in Taylor order to $o(x^6)$

23 votes
Accepted

Two Representations of the Prime Counting Function

23 votes
Accepted

Prove $\int^\infty_0\frac x{e^x-1}dx=\frac{\pi^2}{6}$

23 votes
Accepted

Derivative of Riemann zeta, is this inequality true?

23 votes
Accepted

How to prove by arithmetical means that $\sum\limits_{k=1}^\infty \frac{((k-1)!)^2}{(2k)!} =\frac{1}{3}\sum\limits_{k=1}^{\infty}\frac{1}{k^{2}}$

22 votes
Accepted

How to check convexity?

21 votes
Accepted

How not to prove the Riemann hypothesis

21 votes
Accepted

Easy way of memorizing or quickly deriving summation formulas

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