$P_{n-\frac{1}{2}}^m\left(\cosh \xi \right)=\frac{\Gamma \left(n+m+12\right)}{\Gamma \left(n-m+12\right)}{\left(\frac{2}{\pi \sinh \xi }\right)}^{1/2}{Q}_{m-\frac{1}{2}}^n\left(\coth \xi \right)$