Is the asymptotic expansion of the confluent Heun function known??
The confluent Heun's differential equation is given by
\begin{equation} y''(z) + \left( \epsilon + \frac{\gamma}{z}+ \frac{\delta}{z-1} \right) y'(x) + \left(\frac{\alpha z-q}{z(z-1)} \right) y(z)=0 \end{equation}
One of the solution, $Hc(\epsilon,\delta,\gamma,\alpha,q;z)$ , is defined by $$ Hc(\epsilon,\delta,\gamma,\alpha,q;z=0) = 1 ,\\ Hc'(\epsilon,\delta,\gamma,\alpha,q;z=0) = -\frac{q}{\gamma}.$$
I wonder if the asymptotic expansion of this function at $z\to -\infty$ is known. Thank you so much!