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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
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