A truncated theta identity of Gauss and overpartitions into odd parts (Q2299107)

An overpartition of a positive integer \(n\) is a partition of \(n\) in which the first occurrence of a part of each size may be overlined. The authors examine two truncated series derived from a classical theta identity of Gauss. As a consequence, they obtain two infinite families of inequalities for the overpartition function \(\overline{p}_o (n)\) counting the number of overpartitions into odd parts. The authors provide partition-theoretic interpretations of these results. The last relation of the given corollary provides an efficient algorithm for computing the function \(\overline{p}_o (n)\).