    \begin{align*}
        k:= \max \left\{ \frac{\gamma + \frac{1}{\gamma}}{2} 
        \frac{\gamma + \frac{1}{\gamma}}{2} \left( 1 + \gamma^2 \right)^
        {- \frac{\nu+1}{2}} \right\} 
        = \frac{\gamma + \frac{1}{\gamma}}{2}.
    \end{align*}
