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Closed formula for the capacity of several aligned segments

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Abstract

We present a universal closed formula in terms of theta functions for the Logcapacity 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).

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Authors and Affiliations

  1. Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119333, Russia

    A. B. Bogatyrev & O. A. Grigoriev

  2. Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701, Russia

    A. B. Bogatyrev

  3. Moscow State University, Moscow, 119991, Russia

    A. B. Bogatyrev

Authors
  1. A. B. Bogatyrev
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  2. O. A. Grigoriev
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Correspondence to A. B. Bogatyrev.

Additional information

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Vol. 298, pp. 67–74.

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Bogatyrev, A.B., Grigoriev, O.A. Closed formula for the capacity of several aligned segments. Proc. Steklov Inst. Math. 298, 60–67 (2017). https://doi.org/10.1134/S0081543817060050

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  • DOI: https://doi.org/10.1134/S0081543817060050

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