Abstract
A new analytical method for the conformal mapping of rectangular polygons with a straight angle at infinity to a half-plane and back is proposed. The method is based on the observation that the SC integral in this case is an abelian integral on a hyperelliptic curve, so it may be represented in terms of Riemann theta functions. The approach is illustrated by the computation of 2D-flow of ideal fluid above rectangular underlying surface and the computation of the capacities of multi-component rectangular condensers with axial symmetry.
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Notes
Our notation of theta characteristic as two-column vectors is not universally accepted: some authors use the transposed matrix.
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Communicated by Darren Crowdy.
O. A. Grigor’ev was supported by RSCF Grant 16-11-10349.
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Bogatyrev, A.B., Grigor’ev, O.A. Conformal Mapping of Rectangular Heptagons II. Comput. Methods Funct. Theory 18, 221–238 (2018). https://doi.org/10.1007/s40315-017-0217-z
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DOI: https://doi.org/10.1007/s40315-017-0217-z