The Asymptotic Behavior of a Family of Sequences via Tauberian Theorems |
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Authors: | Patrick Martinez |
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Institution: | a E.N.S. Cachan, Antenne de Bretagne and I.R.M.A.R. Université Rennes I, Campus de Ker Lann, 35 170, Bruz, Francef1 |
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Abstract: | We study the asymptotic behavior of a family of sequences defined by the following nonlinear induction relation c0 = 1 and cn ∑kj = 1 rjcn/mj] + ∑kj = k + 1 rjc(n + 1)1/mj] − 1 for n ≥ 1, where the rj are real positive numbers and mj are integers greater than or equal to 2. Depending on the fact that ∑kj = 1 rj is greater or lower than 1, we prove that cn/nα or cn/(ln n)α goes to some finite limit for some explicit α. Our study is based on Tauberian theorems and extends a result of Erdös et al. |
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Keywords: | Tauberian theorems sequences asymptotic behavior |
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