1993/12/06 by Carl M. Bender, C. M. Bender, Stefan Boettcher +1 · 1 citation
Mathematics · Physics and Astronomy · #Analytic Number Theory Research #Mathematical Approximation and Integration #Mathematical functions and polynomials #hep-lat
paper · pdf · doi:10.1063/1.530577
published as J.Math.Phys. 35 (1994) 1914-1921 · plain TEX, 7 pages, 7 figures included, WASH-U-HEP-93
arxiv created 1993/12/06 · openalex publication_date 1994/04/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A difficult and long-standing problem in mathematical physics concerns the determination of the value of f(∞) from the asymptotic series for f(x) about x=0. In the past the approach has been to convert the asymptotic series to a sequence of Padé approximants Pnn(x) and then to evaluate these approximants at x=∞. Unfortunately, for most physical applications the sequence Pnn(∞) is slowly converging and does not usually give very accurate results. In this paper the results of extensive numerical studies for a large class of functions f(x) associated with strong-coupling lattice approximations are reported. It is conjectured that for large n, Pnn(∞)∼f(∞)+B/ln n. A numerical fit to this asymptotic behavior gives an accurate extrapolation to the value of f(∞).