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Conformal mappings between canonical multiply connected domains. (English) Zbl 1101.30010
The authors show that the modified Green’s function of a multiply connected circular domain can be represented by the Schottky-Klein prime function associated with this domain. Using this result, explicit analytic formulae for the conformal mappings from circular domains to domains with parallel, radial or circular slits are constructed.

MSC:
30C20 Conformal mappings of special domains
31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions
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