Remainder in Asymptotic Expansion of Erfc

Question

According to Abramowitz and Stegun: Handbook of Mathematical Functions (7.1.23 and 7.1.24, http://people.math.sfu.ca/~cbm/aands/page_298.htm), we have Asymptotic expansion of Erfc is given by \begin{align*} \sqrt{\pi}z e^{z^3}\mathrm{erfcz}\sim1+\sum_{m=1}^{\infty}(-1)^m\frac{1.3.\cdots(2m-1)}{(2z^2)^m},\quad\left(z\mapsto\infty,\vert\mathrm{arg}z\vert<\frac{3\pi}{4}\right) \end{align*} The Remainder after $n$ terms is \begin{align*} R_{n}(z)&=(-1)^n\frac{1.3.\cdots(2n-1)}{(2z^2)^n}\int_{0}^{\infty}e^{-t}\left(1+\frac{t}{z^2}\right)^{-n-1/2}~dt. \end{align*} Can Any one explain, can be we get bounds of $ \vert R_{n}(z) \vert $ for complex number $z=a+ i b$ when $\frac{\pi}{2}<\mathrm{arg}(z)<\pi$?.