[math] \newcommand{\mathds}{\mathbb}[/math]

Work out an alternative proof for the main result regarding the truncated characters of the hyperoctahedral group [math]H_N[/math], namely

[[math]] \chi_t\sim e^{-t}\sum_{k=-\infty}^\infty\delta_k\sum_{p=0}^\infty \frac{(t/2)^{|k|+2p}}{(|k|+p)!p!} [[/math]]

with [math]N\to\infty[/math], by working our first an explicit formula for the polynomials integrals over [math]H_N[/math], and then using that for computing the laws of truncated characters.