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Teoreticheskaya i Matematicheskaya Fizika, 1988, Volume 75, Number 2, Pages 234–244 (Mi tmf4777)  

Borel summation of divergent series in field theory and Wynn's $\varepsilon$ algorithm

I. O. Maier
References:
Abstract: The first confluent form of Wynn's $\varepsilon$ algorithm is used in the Borel summation of some divergent perturbation-theory series that satisfy a strong asymptotic condition. The summation procedure reduces to the calculation of a sequence of ratios of Hankel functional determinants composed of a Borel integral and its derivatives and can be regarded as an alternative to the Padé and Padé–Borel methods. It admits a simple generalization to the summation of multiple series. The perturbation series for the ground-state energy of the anharmonic oscillator, Yukawa potential, and charmonium potential are analyzed; the critical exponents of the $O(n)$-symmetric $\varphi^4$ theories (models of phase transitions) for $n=0,1,2,3$ and the dilute Ising model are determined.
Received: 01.10.1986
English version:
Theoretical and Mathematical Physics, 1988, Volume 75, Issue 2, Pages 493–501
DOI: https://doi.org/10.1007/BF01017489
Bibliographic databases:
Language: Russian
Citation: I. O. Maier, “Borel summation of divergent series in field theory and Wynn's $\varepsilon$ algorithm”, TMF, 75:2 (1988), 234–244; Theoret. and Math. Phys., 75:2 (1988), 493–501
Citation in format AMSBIB
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\by I.~O.~Maier
\paper Borel summation of divergent series in field theory and Wynn's~$\varepsilon$ algorithm
\jour TMF
\yr 1988
\vol 75
\issue 2
\pages 234--244
\mathnet{http://mi.mathnet.ru/tmf4777}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=959126}
\transl
\jour Theoret. and Math. Phys.
\yr 1988
\vol 75
\issue 2
\pages 493--501
\crossref{https://doi.org/10.1007/BF01017489}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1988U172900008}
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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