Geodesic
Perturbation theory with convergent series for calculating physical quantities specified by finitely many terms of a divergent series in traditional perturbation theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 3, pp. 452-461

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A new high-accuracy method is suggested for calculating physical quantities for which only finitely many terms of the divergent series in a traditional perturbation theory are known. The method is based on approximating the desired quantity with the sum of finitely many terms of an absolutely convergent series. As an example, the $\beta$-function in the $\varphi_4^4 $ model and the critical exponent $\alpha$ characterizing the behavior of the $\mathrm{He}^4$ heat capacity near the phase transition point are calculated. 
@article{TMF_2000_123_3_a6,
     author = {V. V. Belokurov and Yu. P. Solov'ev and E. T. Shavgulidze},
     title = {Perturbation theory with convergent series for calculating physical quantities specified by finitely many terms of a divergent series in traditional perturbation theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {452--461},
     publisher = {mathdoc},
     volume = {123},
     number = {3},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_123_3_a6/}
}
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V. V. Belokurov; Yu. P. Solov'ev; E. T. Shavgulidze. Perturbation theory with convergent series for calculating physical quantities specified by finitely many terms of a divergent series in traditional perturbation theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 3, pp. 452-461. http://geodesic.mathdoc.fr/item/TMF_2000_123_3_a6/