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Schwarz–Christoffel Mapping from a Rectangle

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Abstract

We investigate the conformal mapping of a rectangle onto a polygon. Using theta elliptic functions, we represent such a mapping via an integral of the Schwarz–Christoffel type; this representation is convenient for finding the conformal modulus of a quadrilateral or a generalized quadrilateral. We also write the Schwarz–Christoffel formula for a mapping from the triangle with angles \(\pi/2\), \(\pi/4\), \(\pi/4\). We present several examples of mapping from a rectangle. Besides, we give an implicit formula for the conformal modulus of a quadrilateral.

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Funding

This work was supported by the Ministry of Science and Higher Education of Russia (agreement no. 075-02-2023-943).

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Authors and Affiliations

  1. Regional Scientific and Educational Mathematical Center, Tomsk State University, Tomsk, Russia

    I. A. Kolesnikov

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  1. I. A. Kolesnikov
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Correspondence to I. A. Kolesnikov.

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Kolesnikov, I.A. Schwarz–Christoffel Mapping from a Rectangle. Lobachevskii J Math 45, 443–451 (2024). https://doi.org/10.1134/S1995080224010256

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  • DOI: https://doi.org/10.1134/S1995080224010256

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