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Abstract: Pairs F(x), G(x) of analytic generating functions that satisfy relations such as 1 +G(x) = exp(F(x)) are studied. It is shown that if F(x) satisfies fairly mild regularity conditions, such as those imposed by Hayman in his study of coefficients of some general classes of functions, then G(x) satisfies the much stricter conditions imposed by Harris and Schoenfeld. This enables one to obtain complete asymptotic expansions for the coefficients of G(x). Applications of this result are made to... (Update)
Context of citations to this paper: More
...(2. 5) However, when P(z , y) is not a polynomial, one can often obtain asymptotic estimates by using more classical estimates [18,19,29]. 3. Average heights of trees In the preceding section we presented some results on the enumeration of trees of a given height, so...
.... function we are studying is entire (has no singularities) or is exponentially growing near its singularity, we can use saddle point methods [Hay56, HS68, OR85]. A somewhat different technique from those we have considered till now is based in Mellin transform. Given a real...
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BibTeX entry: (Update)
Odlyzko, A. M., and Richmond, L. B. Asymptotic expansions for the coefficients of analytic generating functions. Aequationes Mathematicae 28 (1985), 50--63. http://citeseer.ist.psu.edu/odlyzko85asymptotic.html More
@article{ odlyzko85asymptotic,
author = "A. M. Odlyzko and L. B. Richmond",
title = "Asymptotic Expansions for the Coefficients of Analytic Generating Functions",
journal = "Aequationes Mathematicae",
volume = "28",
pages = "50--63",
year = "1985",
url = "citeseer.ist.psu.edu/odlyzko85asymptotic.html" }
Citations (may not include all citations):116 Graphical Enumeration (context) - Harary, Palmer - 1973
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13 A generalization of Stirling's formula (context) - Hayman - 1956
12 Enumerative uses of generating functions (context) - Bender, Goldman - 1971
6 An asymptotic expansion for the coefficients of some formal .. (context) - Bender - 1975
6 An asymptotic expansion for the coefficients of some formal .. (context) - Bender, Richmond
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1 of idempotent elements in the symmetric semigroup on n eleme.. (context) - Harris, Schoenfeld et al. - 1966
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