Abstract
Letf(z) be the generating function of the sequence {p(n)} of unrestricted partitions ofn, and letXtbe an integral random variable taking the valuenwith probability (f(t))−1p(n)tn. It is shown here that, ast→1, the normalizedXtare asymptotically Gaussian. The mode of convergence is sufficiently strong for the conclusion of a local central limit theorem to hold, leading to the classical formula of Hardy–Ramanujan,[formula].
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