Geodesic
Borel summation of divergent series in field theory and Wynn's $\varepsilon$ algorithm
Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 2, pp. 234-244 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {I. O. Maier},
     title = {Borel summation of divergent series in field theory and {Wynn's~}$\varepsilon$ algorithm},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {234--244},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1988_75_2_a7/}
}
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I. O. Maier. Borel summation of divergent series in field theory and Wynn's $\varepsilon$ algorithm. Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 2, pp. 234-244. http://geodesic.mathdoc.fr/item/TMF_1988_75_2_a7/

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