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Some Algebraic Properties Of Asymptotic Power Series

Published online by Cambridge University Press:  20 November 2018

T. E. Hull
T. E. Hull*
Affiliation:
University of British Columbia
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1. Introduction. Let us consider all power series of the form

It was shown first by Borel (1) that to each such series there corresponds a non-empty class of functions such that each function in the class has the given series as its asymptotic expansion about z = 0, the expansion being valid in a sector of the right half z-plane with vertex at the origin.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 220 - 224
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Carleman, T., Les fonctions quasianalytiques (Paris, 1926).Google Scholar
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4. Poincaré, H., Sur les intégrales irregulières des équations linéaires, Acta Math., 8 (1886) 295–344.Google Scholar
5. Popken, J., Asymptotic expansions from an algebraic standpoint, Nederl. Akad. Wetensch. Proc, Ser. A., 56 (Indagationes Math., 15 (1953), 131–143).Google Scholar