# Bounds on the Confluent Hypergeometric Limit Function

I am looking for lower and (primarily) upper bounds on the Confluent Hypergeometric Limit Function ${}_0F_1$

$${}_0F_1(;a;z)=\lim_{q\rightarrow\infty}{}_1F_1\left(q;a;\frac{z}{q}\right)$$

for negative, real values of $z$. For more information, see https://en.wikipedia.org/wiki/Generalized_hypergeometric_function#The_series_0F1

I have found some nontrivial bounds of the ${}_{q+1}F_q$ family, and in particular, of the Hypergeometric Function ${}_2F_1$, in the following paper https://arxiv.org/pdf/math/0703084.pdf. My question is, does there exist similar bounds as, for instance, Eq. (4) in the reference provided, but for the Confluent Hypergeometric Limit Function? In such case, which are those bounds?