  We study subgap transport through an interacting quantum dot tunnel coupled
to one normal and two superconducting leads. To check the reliability of an
approximation of an infinitely-large gap $\Delta$ in the superconducting leads
and weak tunnel coupling to the normal lead, we perform a $1/\Delta$ expansion,
and we analyze next-to-leading order corrections in the tunnel coupling to the
normal lead. Furthermore, we propose a resummation approach to calculate the
Andreev bound states for finite $\Delta$. The results are substantially more
accurate than those obtained by mean-field treatments and favorably compare
with numerical exact results.
