Journal of Number Theory

Volume 38, Issue 2, June 1991, Pages 135-144

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A Hardy-Ramanujan formula for restricted partitions

Dedicated to the Memory of S. Ramanujan

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Gert Almkvist
Mathematics Institute, University of Lund, Box 118, S-221 00 Lund, Sweden
George E. Andrews
Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802 USA

Received 30 November 1988, Revised 27 November 1989, Available online 10 July 2004

Communicated by Hans Zassenhaus

doi:10.1016/0022-314X(91)90079-Q

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Abstract

In this paper, we extend the Hardy-Ramanujan-Rademacher formula for p(n), the number of partitions of n. In particular we provide such formulas for p(j, n), the number of partitions of j into at most n parts and for A(j, n, r), the number of partitions of j into at most n parts each ≤r.
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