We discuss recently developed numerics for the Schwarz–Christoffel transformation for unbounded multiply connected domains. The original infinite product representation for the derivative of the mapping function is replaced by a finite factorization where the inner factors satisfy certain boundary conditions derived here. Least squares approximations based on Laurent series are used to satisfy the boundary conditions. This results in a much more efficient method than the original method based on reflections making the accurate mapping of domains of higher connectivity feasible.