### Abstract

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 φ_{2}^{4} quantum field theory.

Original language | English (US) |
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Pages (from-to) | 261-263 |

Number of pages | 3 |

Journal | Journal of Mathematical Physics |

Volume | 21 |

Issue number | 2 |

DOIs | |

State | Published - 1979 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Sokal, A. D. (1979). An improvement of Watson's theorem on Borel summability.

*Journal of Mathematical Physics*,*21*(2), 261-263. https://doi.org/10.1063/1.524408