An improvement of Watson's theorem on Borel summability

Alan D. Sokal

    Research output: Contribution to journalArticlepeer-review


    Watson's theorem, which gives sufficient conditions for Borel summability, is not optimal. Watson assumes analyticity and uniform asymptotic expansion in a sector |argz|<π/2 + ε, |z| < R, with ε > 0; in fact, only the circular region Re(1/z) > 1/R is required. In particular, one can take ε = 0. This improved theorem gives a necessary and sufficient characterization of a large class of Borel-summable functions. I apply it to the perturbation expansion in the φ24 quantum field theory.

    Original languageEnglish (US)
    Pages (from-to)261-263
    Number of pages3
    JournalJournal of Mathematical Physics
    Issue number2
    StatePublished - 1979

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics


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