Elliptic integrals and the Schwarz-Christoffel transformation
Several aspects of the elliptic integrals in connection with the Schwarz-Christoffel transformation are discussed. An important aspect is the numerical computation of the real elliptic integrals by using series expansions. More complicated complex integrals are also considered. Many details on many aspects of the Schwarz-Christoffel transformation are given. Examples of several polygon mappings are presented graphically, and compared with previous numerically integrated solutions. Remarks: The paper is an important source for polygon conformal mappings. No reference is given to the very efficient real and complex algorithms for computing elliptic integrals of all kinds, as developed by Carlson. See for example \textit{B. C. Carlson} [Numer. Algorithms 10, No. 1-2, 13-26 (1995; Zbl 0827.65024)].
scientific article; zbMATH DE number 1067174
scientific article