Ulrich D Jentschura and Gerhard Soff 2001 J. Phys. A: Math. Gen. 34 1451 doi:10.1088/0305-4470/34/7/316
Ulrich D Jentschura and Gerhard Soff
Show affiliationsThe 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.
30C35 General theory of conformal mappings
81Q15 Perturbation theories for operators and differential equations
Issue 7 (23 February 2001)
Received 26 June 2000
Ulrich D Jentschura and Gerhard Soff 2001 J. Phys. A: Math. Gen. 34 1451
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