\[
\boxed{
 \left( {x}^{2}-1 \right) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) -n \left( n+1 \right) y \left( x \right) +{\frac {\partial }{\partial x}}{\it LegendreQ} \left( n,x \right) =0}
\]