The conformal mapping ω(z) of a domain D onto the unit disc must satisfy the condition |ω(t)| = 1 on ∂D, the boundary of D. The last condition can be considered as a Dirichlet problem for the domain D. In the present paper this problem is reduced to a system of functional equations when ∂D is a circular polygon with zero angles. The mapping is given in terms of a Poincaré series.
@article{bwmeta1.element.bwnjournal-article-apmv68z3p227bwm,
author = {Vladimir Mityushev},
title = {Conformal mapping of the domain bounded by a circular polygon with zero angles onto the unit disc},
journal = {Annales Polonici Mathematici},
volume = {69},
year = {1998},
pages = {227-236},
zbl = {0899.30007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv68z3p227bwm}
}
Vladimir Mityushev. Conformal mapping of the domain bounded by a circular polygon with zero angles onto the unit disc. Annales Polonici Mathematici, Tome 69 (1998) pp. 227-236. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv68z3p227bwm/
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