conformal map regular polygone into unit circle.

From: vanesch@xxxxxx
Date: 20 Sep 2005 07:51:24 -0400

Hi All,

I'm looking for the conformal mapping (using complex functions) that
maps the unit circle (or the upper half plane) into a REGULAR polygon
with n vertices. I know the Schwarz-Christoffel transformation for an
ARBITRARY polygon, but that doesn't help me because the expression is
way too complex to be integrated (I'm trying to find the mapping for a
polygon with 120 vertices). I was hoping that the fact that the polygon
is REGULAR would simplify the problem. I used the mapping on the unit
circle in the S-C transform because out of the symmetry of the problem,
that allowed me (I would guess) to fix the unknown images of the
vertices: they should also be on a regular polygon. But nevertheless, I
cannot solve the integral beyond n = 4.

Any hints, papers, books, ... welcome.

thanks,
Patrick.

.

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