Jack D'Aurizio
I received a master's degree after studying at the University of Pisa and I attended my PhD at the University of Parma, Italy. My menthors are S.Spagnolo, C.Viola and A.Zaccagnini. I worked for a few in Analytic Number Theory, but always had the spot for real analysis, special functions, (analytic) combinatorics and Euclidean geometry.
I am the webmaster of www.matemate.it, which is proud of hosting these notes about elementary Mathematics and dirty tricks. Here it is my (?)best of on MSE:
 A short proof of Stirling's inequality through creative telescoping
 A Ramanujan sum
 The Russian integral
 Fibonacci number that ends with 2014 zeroes
 Fibonacci infinite sum resulting in $\pi$
 An analogue of Hensel lifting for Fibonacci numbers
 An interesting identity involving odd powers of $\pi$
 The sum of $\frac{1}{n\sinh(\pi n\sqrt{3})}$ on odd numbers
 How to prove that $\sum_{k\geq 1}\frac{\zeta(2k)}{2^{2k1}}=1$
 How to distinguish walking on a sphere or on a torus
 Is $\sum_{n\geq 1}\frac{\left\sin n\right^n}{n}$ convergent? (YES it is)
 Sum of squares of harmonic numbers
 A closed form for $\phantom{}_4 F_3\left(1,1,1,\frac{3}{2};\frac{5}{2},\frac{5}{2},\frac{5}{2};1\right)$
 On the largest root of the Hermite polynomial $H_n$
 Fourier transform of squared Gaussian Hermite polynomial
 General formula for the 1;5;19;65;211 sequence
 A NASTY integral of a rational function
 Integral $\int_{0}^{+\infty}\frac{\text{arccot}(\sqrt{x}2\sqrt{x+1})}{x+1}dx$
 Integral $\int_{0}^{\pi}\arctan^2\left(\frac{\sin x}{2+\cos x}\right)dx$
 Different methods to compute $\zeta(2)=\sum_{k\geq 1}\frac{1}{k^2}$ (aka Basel problem)
 On the increasing nature of $x^{x^{x^\ldots}}$ on $\left[1,e^{1/e}\right]$
 A closed form for $\sum_{k\geq 0}\frac{(1)^{k+1}}{k!}\Gamma^2\left(\frac{k}{2}\right)$ (aka the Taylor series of the squared arcsine)

Pisa, Italy

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Last seen Sep 17 at 5:50
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