Sommerfeld–Watson summation of perturbation series
Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 1, pp. 137-145 Cet article a éte moissonné depuis la source Math-Net.Ru

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Conditions are formulated under which a perturbation theory series can be summed by the Sommerfeld–Watson method. A procedure of approximate recovery of the sum of a series is developed. Results are given for some physical problems.
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Yu. A. Kubyshin. Sommerfeld–Watson summation of perturbation series. Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 1, pp. 137-145. http://geodesic.mathdoc.fr/item/TMF_1984_58_1_a10/

[1] Lipatov L. N., ZhETF, 72:2 (1977), 411–427 | MR

[2] Brezin, Le Guillou J. C., Zinn-Justin J., Phys. Rev., D15:6 (1977), 1544–1557 | MR

[3] Bogomolny E. B., Fateev V. A., Lipatov L. N., “Calculation of high orders of perturbation theory in quantum field theory”, Soviet Scientific Reviews, sect. A. Physics Reviews, v. 2, ed. Khalatnikov I. M., 1980, 247–393

[4] Khardi G., Raskhodyaschiesya ryady, IIL, M., 1951, 504 pp. | MR

[5] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki. T. 4. Analiz operatorov, Mir, M., 1982, 428 pp. | MR

[6] Kazakov D. I., Tarasov O. V., Shirkov D. V., TMF, 38:1 (1979), 15–25 | MR

[7] Lipatov L. N., ZhETF, 71:6 (1976), 2010–2024 | MR

[8] Popov V. S., Eletskii V. L., Turbiner A. V., ZhETF, 74:2 (1978), 445–465 | MR

[9] Levin B. Ya., Raspredelenie kornei tselykh funktsii, GITTL, M., 1956, 632 pp. | MR

[10] Kollinz P., Vvedenie v redzhevskuyu teoriyu i fiziku vysokikh energii, Atomizdat, M., 1980, 432 pp.

[11] Dittes F. M., Kubyshin Yu. A., Tarasov O. V., TMF, 37:1 (1978), 66–73 | MR

[12] Baker G. A., Jr., Essentials of Pade approximants, Academic Press, New York, 1975, 306 pp. | MR

[13] Lopes G., Matem. sbornik, 107:1 (1978), 69–83 | MR | Zbl

[14] Vladimirov A. A., Kazakov D. I., Tarasov O. V., ZhETF, 77:3 (1979), 1035–1045 | MR

[15] Le Guillou J. C., Zinn-Justin J., Phys. Rev. Lett., 39:2 (1977), 95–98 | DOI | MR

[16] Kubyshin Yu. A., TMF, 57:3 (1983), 363–372 | MR