THE FORMAL THEORY OF ASYMPTOTIC SERIES

POINCARÉ, HENRI.

Sur les Intégrales irrégulieres des Equations linéaires.

(Berlin, Uppsala & Stockholm, Paris, 1886). 4to. Without wrappers as extracted from "Acta Mathematica. Hrsg. von G. Mittag-Leffler.", Bd. 8, pp. 295-344.

First edition. "The full recognition of the nature of those divergent series that are useful in the representation and calculation of functions and a formal definition of those series wer achieved by Poincaré and Stieltjes independently in 1886. Poincaré called these series asymptotic while Stieltjes continued to use the term semiconvergent. Poincaré took up the subject in order to further the solution of linear differential equations. Impressed by the usefulness of divergent series in astronomy, he sought to determine which were useful and why. he succededed in islolating and formulating the essential property...Poincaré applied his theory of asymptotic series to diffrential equations, and theree are many such uses in his treatise on celestical mechanics, 'Les Methodes nouvelles de la mechanique céleste". (Morris Kline).

Order-nr.: 39132