5 problems

Optimal-measure claim. For any fixed $n\geq 1$, the optimal measure is $d\sigma=w^\lambda dx$ for some $\lambda\in(-1/2,\infty)$. The value of $\lambda$ may depend on $n$.

Let $G$ be a graphical function for which the radial representation and Gegenbauer expansion are defined. Universal Gegenbauer expansion conjecture. The Gegenbauer expansion (gfr)…

Positivity conjecture. $F_n^{\lambda,\delta}(t)>0$ for every $t\in(0,\pi]$ if $\delta\geq\lambda+1$.

For integers $d,q\geq 2$, let $c_{q;d}$ denote the constants arising in the asymptotics of powers of the Gegenbauer polynomials, with … The strict inequality $c_{q;d}>0$ should hol…

Integral positivity conjecture. The inequality $F_n^{\lambda,\delta}(t)>0$ holds for every $n\in\mathbb{N}_0$ and every $t\in(0,\pi]$ if and only if $\delta\geq\lambda+1$.