30,478 reputation
33291
bio website matemate.it
location Pisa, Italy
age
visits member for 2 years
seen 13 mins ago

I received a master's degree after studying at the University of Pisa and I am attending my PhD at the University of Parma, Italy. I work in analytic number theory, and always had the spot for real analysis, special functions, (analytic) combinatorics and euclidean geometry.

I am the webmaster of www.matemate.it.


2d
answered For every $x \in [\frac{\pi}{2},\pi]$, $\sin(x)+\cos(x)\geq 1$. Prove rigorously by contradiction.
2d
answered Limit by L'hospital's rule
2d
answered Proof of $\arcsin x \le 2\arctan x$?
2d
comment Asymptotic approximation of the arctangent?
You could be interested in a recent work of mine: files.ele-math.com/preprints/mia-3585-pre.pdf
Oct
20
answered Prove $a^2\cos B\cos C+b^2\cos C\cos A+c^2\cos A\cos B\leq2S.$
Oct
19
answered Showing that $e^{-2} < \ln 2$
Oct
19
answered Proving convergence of $ \int \limits_0^{\infty} \cos\left(x^2\right) dx $
Oct
19
reviewed Approve suggested edit on convergence criteria of an infinite series
Oct
19
reviewed Approve suggested edit on An asymptotic expression of sum of powers of binomial coefficients.
Oct
19
answered $\sqrt{7}$ ,$\sqrt {7 - \sqrt {7}}$,$\sqrt {7 - \sqrt {7 + \sqrt {7}}}$,$\sqrt{7-\sqrt {7 + \sqrt {7 - \sqrt {7}}}}$, …
Oct
19
answered An asymptotic expression of sum of powers of binomial coefficients.
Oct
18
answered Large $t$ asymptotics of $\int_0^{\infty}\exp(-tx)\exp(-\frac{1}{x^2})dx$
Oct
18
revised Prove $1.43 < \displaystyle \int_0^1 e^{x^2} \mathrm{d}x < \frac{e+1}{2}$
added 69 characters in body
Oct
18
answered How to show that five points in ℝ³ are cospherical?
Oct
18
answered Solve the integral with complex number and floor function.
Oct
17
awarded  Necromancer
Oct
17
awarded  improper-integrals
Oct
16
comment Prove that $2 \le \int_0^1 \ \frac{{(1+x)^{1+x}}}{x^x} \ dx \le 3$
@MarkFischler: sorry, it was a typo, now fixed.
Oct
16
revised Prove that $2 \le \int_0^1 \ \frac{{(1+x)^{1+x}}}{x^x} \ dx \le 3$
deleted 2 characters in body
Oct
16
comment Is $\sum\limits_{\text{p prime}, p \geq 2}\frac{(-1)^{\frac{p^2-1}{8}}}{p}$ convergent or divergent??
@Pablo: the key fact is that the terms corresponding to values of $n\geq 2$ give a bounded contribute, hence $\sum_p\frac{\chi(p)}{p}$ is $\log\left(\sum_{n\geq 1}\frac{\chi(n)}{n}\right)+O(1).$