Abstract
A univalent function is constructed that effects a conformal mapping of an n-connected circular region onto the entire plane with finite cuts along the arcs of logarithmic spirals. An approximate formula is obtained for this function, as well as the corresponding error.
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G. M. Goluzin, “Solution of principal two-dimensional problems of mathematical physics for the case of the Laplace equation and multiply-connected regions bounded by circles,” Mat. Sb.,41, No. 2, 246–276 (1934).
S. V. Goncharenko, “On the approximate Schwarz formula for an n-connected circular region,” Ukr. Mat. Zh.,27, No. 3, 369–373 (1975).
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Translated from Matematicheskie Zametki, Vol. 21, No. 3, pp. 329–334, March, 1977.
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Dunduchenko, L.E., Goncharenko, S.V. Mapping of n-connected region onto a plane with cuts along the arcs of logarithmic spirals. Mathematical Notes of the Academy of Sciences of the USSR 21, 183–185 (1977). https://doi.org/10.1007/BF01106741
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DOI: https://doi.org/10.1007/BF01106741