$H_{\lambda }^{*}=\left({\prod }_{i=1}^k{n}_i!\right){\prod }_{i<j}\frac{n_i+n_j}{n_i-n_j}=2^{-\frac{k}{2}}\sqrt{H_{\tilde{\lambda }}},\frac{1}{\sqrt{H_{\tilde{\lambda }}}}=\sqrt{s_{\tilde{\lambda }}\left(t_{\infty }\right)}=2^{-\frac{k}{2}}{Q}_{\lambda }\left(\frac{t_{\infty }}{2}\right)$