Approximate Block Method of Conformal Mapping of Polygons onto Canonical Domains

Suppose that in the complex plane zy z = x + iy, there is an open simply-connected polygon i! (see Sec. 1), to be conformally mapped onto a unit disk \(\ < 1, ( = £ -f ¿77, so that a point z0 belonging to ii passes into the center of the disk. The required mapping function C = f ( z ) 1S known (see [23, item 43]) to be representable in the form

( 11.1)

where u is a solution of Dirichlet’s problem

v is a harmonic function conjugate to u, and (3 is an arbitrary con­ stant.