Two truncated identities of Gauss
Combinatorics
2013-01-15 v2 Number Theory
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.
Keywords
Cite
@article{arxiv.1205.4340,
title = {Two truncated identities of Gauss},
author = {Victor J. W. Guo and Jiang Zeng},
journal= {arXiv preprint arXiv:1205.4340},
year = {2013}
}
Comments
9 pages, final version