5 problems

Let $m$ be the complex dimension, let $m\leq q\leq 2m$, and let $Y_{2m-q}$, $\Delta(\lambda)$, $\Delta(\xi)$ and the integration variables be as in the source's preceding definitio…

Let $G$ be a finite reflection group acting on $\mathbb{R}^k$, let $P(s)$ be the product of the distances from $s=(s_1,\ldots,s_k)$ to all reflecting hyperplanes of $G$, and let…

Vanishing integral conjecture. The integral $I_{\lambda}(a,b;q,t,t^n)$ vanishes unless $\operatorname{2\text{-}core}(\lambda)=0$. Moreover, the two specializations satisfy

Cauchy–Schlömilch formula explanation conjecture. We conjecture that these two results follow from the Cauchy–Schlömilch formula.

The sum-rule conjecture. For every such pair $(n,k)$,