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On an elementary proof of some asymptotic formulas in the theory of partitions. (English) Zbl 0061.07905
Let $p(n)$ be the number of partitions of the positive integer $n$ and let $p_k(n)$ be the number of partitions of $n$ into exactly $k$ summands. The author gives an elementary proof that $\lim_{n \to \infty} n p(n) \exp\{-\pi(2n/3)^{1/2}\}$ exists and is positive, but does not determine its value (known to be $48^{-1/2}$). An elementary determination of the value of the limit was later given by {\it D.J.Newman} (Zbl 0043.04501).
Reviewer: P.T.Bateman

11P82Analytic theory of partitions
11P81Elementary theory of partitions
number theory
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