  A generalization of the Schwarz-Christoffel mapping to multiply connected
polygonal domains is obtained by making a combined use of two preimage domains,
namely, a rectilinear slit domain and a bounded circular domain. The conformal
mapping from the circular domain to the polygonal region is written as an
indefinite integral whose integrand consists of a product of powers of the
Schottky-Klein prime functions, which is the same irrespective of the preimage
slit domain, and a prefactor function that depends on the choice of the
rectilinear slit domain. A detailed derivation of the mapping formula is given
for the case where the preimage slit domain is the upper half-plane with radial
slits. Representation formulae for other canonical slit domains are also
obtained but they are more cumbersome in that the prefactor function contains
arbitrary parameters in the interior of the circular domain.
