# A Theory of Asymptotic Series

@article{WatsonATO, title={A Theory of Asymptotic Series}, author={George Neville Watson}, journal={Philosophical Transactions of the Royal Society B} }

In their efforts to place mathematical analysis on the firm est possible foundations, Abel and Cauchy found it necessary to banish non-convergent series from their work ; from that time until a quarter of a century ago the theory o f divergent series was, in general, neglected by mathematicians. A consistent theory of divergent series was, however, developed by Poincare in 1886, and, ten years later, Borel enunciated his theory of summability in connection with oscillating series. So far as…

## 79 Citations

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A family of formal power series, such that its coefficients satisfy a recursion formula, is characterized in terms of the summability, in the sense of J. P. Ramis, of its elements along certain well…

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We give a relatively short, almost self-contained proof of the fact that the partition function of the suitably renormalised Φ 43 measure admits an asymptotic expansion, the coefﬁcients of which…

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We present a maximal class of analytic functions, elements of which are in one-to-one correspondence with their asymptotic expansions. In recent decades it has been realized (B. Malgrange, J. Ecalle,…

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### Growth estimates for the coefficients of generalized formal solutions, and representation of solutions using Laplace integrals and factorial series

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