Let $m$ and $n$ be two positive integers and denote by $P(n,m)$ the number of partitions of $n$ into $m$ non-negative integers.


Is there an asymptotic formula for $P(n,m)$ ?? Any reference is welcome. Thanks



asymptotic for restricted partitions
For $m\geq n^{1/6}$ there is an asymptotic formula due to Szekeres. See <http://www.combinatorics.org/ojs/index.php/eljc/article/view/v4i2r6/pdf> for references and another proof.


