English

An upper bound for the logarithmic capacity of two intervals

Complex Variables 2013-06-27 v1

Abstract

The logarithmic capacity (also called Chebyshev constant or transfinite diameter) of two real intervals [1,α][β,1][-1,\alpha]\cup[\beta,1] has been given explicitly with the help of Jacobi's elliptic and theta functions already by Achieser in 1930. By proving several inequalities for these elliptic and theta functions, an upper bound for the logarithmic capacity in terms of elementary functions of α\alpha and β\beta is derived.

Keywords

Cite

@article{arxiv.1306.6182,
  title  = {An upper bound for the logarithmic capacity of two intervals},
  author = {Klaus Schiefermayr},
  journal= {arXiv preprint arXiv:1306.6182},
  year   = {2013}
}
R2 v1 2026-06-22T00:40:31.629Z