\[A_{n}\left(-z\right)=\begin{cases}2\sqrt{p/\pi}\cos\left(\tfrac{1}{2}p\pi%
\right)z^{-n/4}\left(\cos\left(\zeta-\tfrac{1}{4}\pi\right)+e^{|\Im\zeta|}O%
\left(\zeta^{-1}\right)\right),&\text{$|\operatorname{ph}z|\leq 2p\pi-\delta$,%
 $n$ odd},\\
\sqrt{p/\pi}z^{-n/4}e^{\zeta}\left(1+O\left(\zeta^{-1}\right)\right),&\text{$|%
\operatorname{ph}z|\leq p\pi-\delta$, $n$ even},\end{cases}\]