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On the Parameter Problem of the Schwarz–Christoffel Mapping and Moduli of Quadrilaterals

On the Parameter Problem of the Schwarz–Christoffel Mapping and Moduli of Quadrilaterals We analyze the Schwarz–Christoffel mapping with emphasis on its geometric properties and apply it to give an algorithm for numerical computation of the modulus of a polygonal quadrilateral. We represent the generalized modulus of the quadrilaterals by formal power series and give an algorithm for the computation of its coefficients by a hypergeometric function in a special case. To illustrate the effectiveness of the algorithm some computational results are given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

On the Parameter Problem of the Schwarz–Christoffel Mapping and Moduli of Quadrilaterals

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References (15)

Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-022-00476-y
Publisher site
See Article on Publisher Site

Abstract

We analyze the Schwarz–Christoffel mapping with emphasis on its geometric properties and apply it to give an algorithm for numerical computation of the modulus of a polygonal quadrilateral. We represent the generalized modulus of the quadrilaterals by formal power series and give an algorithm for the computation of its coefficients by a hypergeometric function in a special case. To illustrate the effectiveness of the algorithm some computational results are given.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 1, 2024

Keywords: Schwarz–Christoffel mapping; Hypergeometric function; Quadrilateral; Conformal modulus; 30C62; 33E05

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