Partitions without small parts (Q2483714)

\textit{J. L. Nicolas} and \textit{A. Sárközy} [J. Théor. Nombres Bordx. 12, No. 1, 227--254 (2000; Zbl 1005.11049)] gave an asymptotic estimate for the number \(r(n, m)\) of partitions of \(n\) into parts, each of which is at least \(m\). Their estimate involves a parameter \(\sigma\) that is defined implicitly in terms of \(n\) and \(m\). The present paper uses the Euler-Maclaurin formula to eliminate \(\sigma\) and gives an asymptotic formula for \(r(n, m)\) in terms of \(n\) and \(m\) only, which is valid for \(m = O(n)\) and \(n\to\infty\).