期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2008
卷号：2008
DOI：10.1155/2008/350326
出版社：Hindawi Publishing Corporation
摘要：The classical Schwarz-Christoffel formula gives conformal mappings of the upper half-plane onto domains whose boundaries consist of a finite number
of line segments. In this paper, we explore extensions to boundary curves
which in one sense or another are made up of infinitely many line segments,
with specific attention to the “infinite staircase” and to the Koch snowflake,
for both of which we develop explicit formulas for the mapping function and
explain how one can use standard mathematical software to generate corresponding
graphics. We also discuss a number of open questions suggested
by these considerations, some of which are related to differentials on hyperelliptic
surfaces of infinite genus.
