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The asymptotic optimal partition and extensions of the Nonsubstitution Theorem

✍ Scribed by Julio-Roberto Hasfura-Buenaga; Allen Holder; Jeffrey Stuart


Book ID
108198741
Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
315 KB
Volume
394
Category
Article
ISSN
0024-3795

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Hardy–Ramanujan's Asymptotic Formula for
✍ Luis BΓ‘ez-Duarte πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 668 KB

Let f (z) be the generating function of the sequence [ p(n)] of unrestricted partitions of n, and let X t be an integral random variable taking the value n with probability ( f (t)) &1 p(n) t n . It is shown here that, as t Γ„ 1, the normalized X t are asymptotically Gaussian. The mode of convergence