\[\widehat{\mathsf{Q}}^{-\mu}_{-\frac{1}{2}+\mathrm{i}\tau}\left(x\right)=\frac{%
\pi e^{-\tau\pi}\sin\left(\mu\pi\right)\sinh\left(\tau\pi\right)}{2({\cosh}^{2%
}\left(\tau\pi\right)-{\sin}^{2}\left(\mu\pi\right))}\mathsf{P}^{-\mu}_{-\frac%
{1}{2}+\mathrm{i}\tau}\left(x\right)+\frac{\pi(e^{-\tau\pi}{\cos}^{2}\left(\mu%
\pi\right)+\sinh\left(\tau\pi\right))}{2({\cosh}^{2}\left(\tau\pi\right)-{\sin%
}^{2}\left(\mu\pi\right))}\mathsf{P}^{-\mu}_{-\frac{1}{2}+\mathrm{i}\tau}\left%
(-x\right).\]