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Sums and series

E Caliceti, M Meyer-Hermann, P Ribeca, A Surzhykov, U Jentschura, From useful algorithms for slowly convergent series to physical predictions based on divergent perturbative expansions, PR 446, 1 (2007) – doi

Suslov I M, Divergent perturbation series, JETP 100, 1188 (2005)

Рамис Ж-П, Расходящиеся ряды и асимптотические теории (ИКИ, 2002)

Balser W, From divergent series to analytic functions, LNM 1582 (1994)

Казаков Д И, Ширков Д В, Суммирование асимптотических рядов в квантовой теории поля (Дубна, 1980)

Барон С, Введение в теорию суммируемости рядов (Таллин, 1977)

Харди Г, Расходящиеся ряды (М., 1951)


A Guttmann, Series extension: predicting approximate series coefficients from a finite number of exact coefficients, JPA 49, 415002 (2016) – doi

Kleinert H, Yukalov V I, Self-similar variational perturbation theory for critical exponents, PRE 71, 026131 (2005)

Yukalov V I, Gluzman S, Sornette D, Summation of power series by self-similar factor approximants, PA 328, 409 (2003)

Rawlinson A A, Converting a series in λ to a series in λ-1, JPA 36, 10215 (2003)

Meurice Y, Simple method to make asymptotic series of Feynman diagrams converge, PRL 88, 141601 (2002)

Bandyopadhyay S K, Bhattacharyya K, Improved methods of estimating critical indices via fractional calculus, JPA 35, 4429 (2002)

Ogreid O M, Osland P, Some infinite series related to Feynman diagrams, J Comput Appl Math 140, 659 (2002)

Kneur J-L, Pinto M B, Ramos R O, Convergent resummed linear δ expansion in the critical O(N) φ4 model, PRL 89, 210403 (2002)

Ehrhardt G C M, Bray A J, Series expansion calculation of persistence exponents, PRL 88, 070601 (2002)

Jasch F, Kleinert H, Fast-convergent resummation algorithm and critical exponents of φ4-theory in three dimensions, JMP 42, 52 (2001)

Суслов И М, О функции Гелл-Манна-Лоу теории φ4, ПЖЭТФ 71, 315 (2000)

Miscellaneous

Кашин В С, Саакян А А, Ортогональные ряды (М., АФЦ, 1999)


Stilck J F, Dickman R, Vidigal R R, Series expansion for a stochastic sandpile, JPA 37, 1145 (2004)