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تسجيل مستخدم جديدA generalized Hardy-Ramanujan formula for the number of restricted integer partitions
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We derive the asymptotic formula for $p_n(N,M)$, the number of partitions of integer $n$ with part size at most $N$ and length at most $M$. We consider both $N$ and $M$ are comparable to $sqrt{n}$. This is an extension of the classical Hardy-Ramanujan formula and Szekeres formula. The proof relies on the saddle point method.
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