Integral and differential equations for conformal mapping of bounded multiply connected regions onto a disk with circular slits

Conformal mapping is a useful tool in science and engineering. On the other hand exact mapping functions are unknown except for some special regions. In this paper we present a new boundary integral equation with classical Neumann kernel associated to f?/f, where f is a conformal mapping of bounded multiply connected regions onto a disk with circular slit domain. This boundary integral equation is constructed from a boundary relationship satisfied by a function analytic on a multiply connected region. With f?/f known, one can then treat it as a differential equation for computing f