Improved conformal mapping of the Borel plane

Ulrich D. Jentschura, Gerhard Soff

Research output: Contribution to journalArticle

13 Citations (Scopus)


The conformal mapping of the Borel plane can be utilized for the analytic continuation of the Borel transform to the entire positive real semi-axis and is thus helpful in the resummation of divergent perturbation series in quantum field theory. We observe that the convergence can be accelerated by the application of Padé approximants to the Borel transform expressed as a function of the conformal variable, i.e. by a combination of the analytic continuation via conformal mapping and a subsequent numerical approximation by rational approximants. The method is primarily useful in those cases where the leading (but not sub-leading) large-order asymptotics of the perturbative coefficients are known.

Original languageEnglish
Pages (from-to)1451-1457
Number of pages7
JournalJournal of Physics A: Mathematical and General
Issue number7
Publication statusPublished - Feb 23 2001

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

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