\[Q^{\mu}_{\nu}\left(x\right)=e^{\mu\pi i}\frac{\pi^{1/2}\Gamma\left(\nu+\mu+1%
\right)\left(x^{2}-1\right)^{\mu/2}}{2^{\nu+1}x^{\nu+\mu+1}}\mathbf{F}\left(%
\tfrac{1}{2}\nu+\tfrac{1}{2}\mu+1,\tfrac{1}{2}\nu+\tfrac{1}{2}\mu+\tfrac{1}{2}%
;\nu+\tfrac{3}{2};\frac{1}{x^{2}}\right),\]