Abstract:
In this paper, some progress has been made in solving the problem of calculating the parameters of the Schwarz–Christoffel integral realizing a conformal mapping of a canonical domain onto a polygon. It is shown that an effective solution of this problem can be found by applying the formulas of analytic continuation of the Lauricella function F(N)D, which is a hypergeometric function of N complex variables. Several new formulas for such a continuation of the function F(N)D are presented that are oriented to the calculation of the parameters of the Schwarz–Christoffel integral in the “crowding” situation. An example of solving the parameter problem for a complicated polygon is given.
Keywords:
Schwarz–Christoffel integral, hypergeometric functions of many variables, analytic continuation, crowding.
Citation:
S. I. Bezrodnykh, “Lauricella Function and the Conformal Mapping of Polygons”, Mat. Zametki, 112:4 (2022), 500–520; Math. Notes, 112:4 (2022), 505–522
\Bibitem{Bez22}
\by S.~I.~Bezrodnykh
\paper Lauricella Function and the Conformal Mapping of Polygons
\jour Mat. Zametki
\yr 2022
\vol 112
\issue 4
\pages 500--520
\mathnet{http://mi.mathnet.ru/mzm13694}
\crossref{https://doi.org/10.4213/mzm13694}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4538786}
\transl
\jour Math. Notes
\yr 2022
\vol 112
\issue 4
\pages 505--522
\crossref{https://doi.org/10.1134/S0001434622090218}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85140307659}
Linking options:
https://www.mathnet.ru/eng/mzm13694
https://doi.org/10.4213/mzm13694
https://www.mathnet.ru/eng/mzm/v112/i4/p500
This publication is cited in the following 6 articles:
S. I. Bezrodnykh, “Generalizations of the Jacobi identity to the case of the Lauricella function FD(N)”, Integral Transforms and Special Functions, 2024, 1
S. I. Bezrodnykh, “Applying Lauricella's function to construct conformal mapping of polygons' exteriors”, Math. Notes, 116:6 (2024), 1183–1203
S. I. Bezrodnykh, “Constructing basises in solution space of the system of equations for the Lauricella Function F(N)D”, Integral Transforms and Special Functions, 34:11 (2023), 813
A. Posadskii, S. Nasyrov, “One-parameter families of conformal mappings of the half-plane onto polygonal domains with several slits”, Lobachevskii J. Math., 44:4 (2023), 1448
S. L. Skorokhodov, “Conformal mapping of a Z-shaped domain”, Comput. Math. Math. Phys., 63:12 (2023), 2451–2473
S. I. Bezrodnykh, “Formulas for computing Euler-type integrals and their application to the problem of constructing a conformal mapping of polygons”, Comput. Math. Math. Phys., 63:11 (2023), 1955–1988
Citation in format AMSBIB
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