4 problems

Let $z\in\mathbb{C}$ satisfy $\Re(z)>-2$. Complex-parameter generalization of Sondow's formula. One should have … For non-negative integers $z=n$, the identity follows from the pre…

For each integer $m\ge 1$, let $c_{2,m}$, $e_{2,m}$, $d_{1,m}$, and $f_{1,m}$ be the numbers appearing in Theorems and. Coefficient relations. The following identities hold: … and…

Let $\Omega_N$ be the space of monic real polynomials of degree $N$ whose roots lie in the interval $[-1,1]$, equipped with volume $D_N$, and let $P$ denote a random polynomial in…

Let $a,b,c,d$ be real numbers, and let … be the discriminant of the cubic polynomial $ax^{3}+bx^{2}+cx+d$. Fujii's real cubic-integral conjecture. The formula … should hold for a c…