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Conformal mapping of the domain bounded by a circular polygon with zero angles onto the unit disc. (English) Zbl 0899.30007
Author’s summary: “The conformal mapping $$\omega(z)$$ of a domain $$D$$ onto the unit disc must satisfy the condition $$|\omega (t)|=1$$ on $$\partial D$$, 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 $$\partial D$$ is a circular polygon with zero angles. The mapping is given in terms of a Poincaré series”.
##### MSC:
 30C20 Conformal mappings of special domains 30E25 Boundary value problems in the complex plane
##### Keywords:
Dirichlet problem; Poincaré series
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