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 Tr. Mat. Inst. Steklova, 2017, Volume 298, Pages 67–74 (Mi tm3803)

Closed Formula for the Capacity of Several Aligned Segments

A. B. Bogatyrevabc, O. A. Grigorieva

a Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119333 Russia
b Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701 Russia
c Moscow State University, Moscow, 119991 Russia

Abstract: We present a universal closed formula in terms of theta functions for the Log-capacity of several segments on a line. The formula for two segments was obtained by N. Achieser (1930); three segments were considered by T. Falliero and A. Sebbar (2001).

 Funding Agency Grant Number Russian Science Foundation 16-11-10349 This work is supported by the Russian Science Foundation under grant 16-11-10349.

DOI: https://doi.org/10.1134/S0371968517030050

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English version:
Proceedings of the Steklov Institute of Mathematics, 2017, 298, 60–67

Bibliographic databases:

UDC: 517.54
MSC: 30C85, 14H42, 31A15, 30Fxx

Citation: A. B. Bogatyrev, O. A. Grigoriev, “Closed Formula for the Capacity of Several Aligned Segments”, Complex analysis and its applications, Collected papers. On the occasion of the centenary of the birth of Boris Vladimirovich Shabat, 85th anniversary of the birth of Anatoliy Georgievich Vitushkin, and 85th anniversary of the birth of Andrei Aleksandrovich Gonchar, Tr. Mat. Inst. Steklova, 298, MAIK Nauka/Interperiodica, Moscow, 2017, 67–74; Proc. Steklov Inst. Math., 298 (2017), 60–67

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3803
• https://doi.org/10.1134/S0371968517030050
• http://mi.mathnet.ru/eng/tm/v298/p67

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This publication is cited in the following articles:
1. 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
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