Geodesic
Analytic Properties of Power Product Expansions
Canadian journal of mathematics, Tome 47 (1995) no. 6, pp. 1219-1239

Voir la notice de l'article provenant de la source Cambridge University Press

Let ƒ(z) be a complex function analytic in some neighbourhood of the origin with ƒ(0) = 1. It is known that ƒ(z) admits a unique "power product" expansion of the form convergent near zero. We derive a simple direct bound for the radius of convergence of this product expansion in terms of the coefficients of ƒ(z). In addition we show that the same bound holds in the case of "inverse power product" expansions Examples are given for which these bounds are sharp. We show also that products with nonnegative coefficients have the same radius of convergence as their corresponding series.
DOI : 10.4153/CJM-1995-062-9
Mots-clés : 41A10, 30E10 
Gingold, H.; Knopfmacher, A. Analytic Properties of Power Product Expansions. Canadian journal of mathematics, Tome 47 (1995) no. 6, pp. 1219-1239. doi: 10.4153/CJM-1995-062-9
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1995-062-9/}
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