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A Hardy–Ramanujan–Rademacher-type formula for (r,s)-regular partitions

✍ Scribed by James Mc Laughlin, Scott Parsell

Book ID: 113078633
Publisher: Springer US
Year: 2012
Tongue: English
Weight: 661 KB
Volume: 28
Category: Article
ISSN: 1382-4090
DOI: 10.1007/s11139-011-9365-3

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📜 SIMILAR VOLUMES

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✍ Gert Almkvist; George E. Andrews 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 335 KB

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Hardy–Ramanujan's Asymptotic Formula for Partitions and the Central Limit Theorem

✍ Luis Báez-Duarte 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 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 Ä 1, the normalized X t are asymptotically Gaussian. The mode of convergence