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Sbornik: Mathematics, 2012, Volume 203, Issue 12, Pages 1715–1735
DOI: https://doi.org/10.1070/SM2012v203n12ABEH004284
(Mi sm8087)
 

This article is cited in 18 scientific papers (total in 18 papers)

Conformal mapping of rectangular heptagons

A. B. Bogatyrevabc

a Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow
b Moscow Institute of Physics and Technology
c M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
References:
Abstract: A new effective approach to calculating the direct and inverse conformal mapping of rectangular polygons onto a half-plane is put forward; it is based on the use of Riemann theta functions.
Bibliography: 14 titles.
Keywords: Christoffel-Schwarz integral, Riemann surface, Jacobian, Siegel space, theta functions.
Received: 22.11.2011
Bibliographic databases:
Document Type: Article
UDC: 517.542+517.545
MSC: Primary 14H42, 30A24, 30A28; Secondary 14H15
Language: English
Original paper language: Russian
Citation: A. B. Bogatyrev, “Conformal mapping of rectangular heptagons”, Sb. Math., 203:12 (2012), 1715–1735
Citation in format AMSBIB
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\paper Conformal mapping of rectangular heptagons
\jour Sb. Math.
\yr 2012
\vol 203
\issue 12
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Linking options:
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  • https://doi.org/10.1070/SM2012v203n12ABEH004284
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  • Related presentations:
    This publication is cited in the following 18 articles:
    1. S. I. Bezrodnykh, “Applying Lauricella's function to construct conformal mapping of polygons' exteriors”, Math. Notes, 116:6 (2024), 1183–1203  mathnet  crossref  crossref
    2. 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  mathnet  mathnet  crossref  crossref
    3. I. S. Polyanskii, K. O. Loginov, “Priblizhennyi metod resheniya zadachi konformnogo otobrazheniya proizvolnogo mnogougolnika na edinichnyi krug”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:1 (2022), 107–129  mathnet  crossref  mathscinet
    4. S. I. Bezrodnykh, “Lauricella Function and the Conformal Mapping of Polygons”, Math. Notes, 112:4 (2022), 505–522  mathnet  crossref  crossref  mathscinet
    5. M. Smirnov, “On the solution of a conformal mapping problem by means of Weierstrass functions”, Comput. Math. Math. Phys., 62:5 (2022), 797–810  mathnet  mathnet  crossref  crossref  scopus
    6. A. B. Bogatyrev, O. A. Grigor'ev, “Filtration under a Stepped Dam and Riemann Theta Functions”, Proc. Steklov Inst. Math., 311 (2020), 10–21  mathnet  crossref  crossref  mathscinet  isi  elib
    7. Bezrodnykh S., Bogatyrev A., Goreinov S., Grigor'ev O., Hakula H., Vuorinen M., “On Capacity Computation For Symmetric Polygonal Condensers”, J. Comput. Appl. Math., 361 (2019), 271–282  crossref  mathscinet  zmath  isi
    8. T. Ayano, V. M. Buchstaber, “Ultraelliptic integrals and two-dimensional sigma-functions”, Funct. Anal. Appl., 53:3 (2019), 157–173  mathnet  crossref  crossref  mathscinet  isi  elib
    9. Bogatyrev A.B. Grigor'ev O.A., “Conformal Mapping of Rectangular Heptagons II”, Comput. Methods Funct. Theory, 18:2 (2018), 221–238  crossref  mathscinet  zmath  isi  scopus
    10. S. I. Bezrodnykh, “The Lauricella hypergeometric function F(N)DF(N)D, the Riemann–Hilbert problem, and some applications”, Russian Math. Surveys, 73:6 (2018), 941–1031  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. S. I. Bezrodnykh, “Analytic continuation of the Appell function F1F1 and integration of the associated system of equations in the logarithmic case”, Comput. Math. Math. Phys., 57:4 (2017), 559–589  mathnet  crossref  crossref  mathscinet  isi  elib
    12. A. B. Bogatyrev, O. A. Grigoriev, “Closed Formula for the Capacity of Several Aligned Segments”, Proc. Steklov Inst. Math., 298 (2017), 60–67  mathnet  crossref  crossref  isi  elib
    13. A. B. Bogatyrev, S. A. Goreinov, S. Yu. Lyamaev, “Analytical approach to multiband filter synthesis and comparison to other approaches”, Problems Inform. Transmission, 53:3 (2017), 260–273  mathnet  crossref  isi  elib
    14. A. B. Bogatyrev, S. A. Goreinov, S. Yu. Lyamaev, “Efficient synthesis of optimal multiband filter”, Russian J. Numer. Anal. Math. Modelling, 32:4 (2017), 217–223  crossref  mathscinet  zmath  isi  scopus
    15. A. B. Bogatyrev, “Image of Abel–Jacobi map for hyperelliptic genus 3 and 4 curves”, J. Approx. Theory, 191 (2015), 38–45  crossref  mathscinet  zmath  isi  elib  scopus
    16. O. A. Grigorev, N. V. Klyushnev, “Primenenie chislenno-analiticheskogo metoda konformnogo otobrazheniya dlya postroeniya setki v orebrennom kanale”, Vychislitelnye metody i programmirovanie: novye vychislitelnye tekhnologii, 15:3 (2014), 487–498  mathnet  elib
    17. S. I. Bezrodnykh, V. I. Vlasov, “Singular Riemann–Hilbert problem in complex-shaped domains”, Comput. Math. Math. Phys., 54:12 (2014), 1826–1875  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    18. O. A. Grigor'ev, “Numerical-analytical method for conformal mapping of polygons with six right angles”, Comput. Math. Math. Phys., 53:10 (2013), 1447–1456  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:709
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    References:71
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