\[\frac{e^{\pm\pi ia}}{2i\sin\left(\pi a\right)}Q\left(-a,ae^{\pm\pi i}\right)%
\sim\pm\frac{1}{2}-\frac{i}{\sqrt{2\pi a}}\sum_{k=0}^{\infty}c_{k}(0)(-a)^{-k},\]