On the Parameter Problem of the Schwarz-Christoffel Mapping and Moduli of Quadrilaterals

We analyze the Schwarz-Christoffel mapping with emphasis on its geometric properties and apply it to give an algorithm for numerical computation of the modulus of a polygonal quadrilateral. We represent the generalized modulus of the quadrilaterals by formal power series and give an algorithm for the computation of its coefficients by a hypergeometric function in a special case. To illustrate the effectiveness of the algorithm some computational results are given.