Two truncated identities of Gauss

被引：71

作者：

Guo, Victor J. W. ^{[1
]}

Zeng, Jiang ^{[2
]}

机构：

[1] E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China

[2] Univ Lyon 1, Inst Camille Jordan, UMR 5208, CNRS, F-69622 Villeurbanne, France

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2013年 / 120卷 / 03期

关键词：

Partition function; Overpartition function; Gauss' identities; Shanks' identity; PARTITIONS;

D O I：

10.1016/j.jcta.2012.12.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 (p) over bar (n) and for the partition function pod(n) counting the partitions of n with distinct odd parts. Some further inequalities for variations of partition function are proposed as conjectures. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：700 / 707

页数：8

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