Two truncated identities of Gauss
arXiv:1205.4340 · doi:10.1016/j.jcta.2012.12.004
Abstract
Two new expansions for partial sums of Gauss' triangular and square numbers series are given. As a consequence, we derive a family of inequalities for the overpartition function and for the partition function counting the partitions of with distinct odd parts. Some further inequalities for variations of partition function are proposed as conjectures.
9 pages, final version