A. B. Bogatyrev, O. A. Grigoriev, “Closed Formula for the Capacity of Several Aligned Segments”, Trudy Mat. Inst. Steklova, 2017, Volume 298,Pages <nobr>67

This article is cited in 3 papers

Closed Formula for the Capacity of Several Aligned Segments

A. B. Bogatyrev^abc, O. A. Grigoriev^a

^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).

Keywords: capacity, theta functions, closed formula.

UDC: 517.54

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

Received: November 21, 2016

DOI: 10.1134/S0371968517030050