Conformal Mapping of Unbounded Multiply Connected Regions onto Logarithmic Spiral Slit with Infinite Straight Slit

This paper presents a boundary integral equation method with the adjoint generalized Neumann kernel for conformal mapping of unbounded multiply connected regions. The canonical region is the entire complex plane bounded by an infinite straight slit on the line Im omega = 0 and finite logarithmic spiral slits. Some linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on a multiply connected region. These integral equations are uniquely solvable. The kernel involved in these integral equations is the adjoint generalized Neumann kernel.