  In this paper we compute b-functions (or Bernstein-Sato polynomials) of
various semi-invariants of quivers. The main tool is an explicit relation for
the b-functions between semi-invariants that correspond to each other under
reflection functors (or castling transforms). This enables us to compute
recursively the b-functions for all Dynkin quivers, and extended Dynkin quivers
with prehomogeneous dimension vectors.
