2013/06/26 by Klaus Schiefermayr, Schiefermayr, Klaus
Mathematics · #Alpha (finance) #Analytic and geometric function theory #Combinatorics #Computer science #Conjecture #Constant (computer programming) #Elliptic integral #Jacobi elliptic functions #Logarithm #Mathematical Inequalities and Applications #Mathematical analysis #Mathematical functions and polynomials #Mathematics #Pure mathematics #Statistics #Transfinite number #Upper and lower bounds #math.CV
paper · pdf · doi:10.48550/arxiv.1306.6182
arxiv created 2013/06/26 · openalex publication_date 2013/06/26 · arxiv updated 2013/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The logarithmic capacity (also called Chebyshev constant or transfinite diameter) of two real intervals [-1,α]∪[β,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 and β is derived.