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
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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.
@article{TMF_1988_75_2_a7,
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},
publisher = {mathdoc},
volume = {75},
number = {2},
year = {1988},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1988_75_2_a7/}
}
TY - JOUR AU - I. O. Maier TI - Borel summation of divergent series in field theory and Wynn's~$\varepsilon$ algorithm JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1988 SP - 234 EP - 244 VL - 75 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1988_75_2_a7/ LA - ru ID - TMF_1988_75_2_a7 ER -
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/