The Extended Legendre-Stirling Numbers of the First Kind

摘要：

　　The Legendre-Stirling numbers of the first kind PSn(j) are defined by the coefficients of Taylor expansion of the function x(x-2)(x-6)…(x(n-1)n) by Andrews and Littlejohn (see A combinatorial interpretation of the Legendre-Stirling numbers,Proc.Amer.Math.Soc,137: 2581-2590,2009).In this paper,two new kinds of numbers PS(j)-n(n≥0,j≥-1) and PS(j)-n(0≤n≤j) which are proposed with the coefficients of Laurent expansion of the function( x(x-2)(x-6)…(x-(n-1)n)-1,which are called the extended Legendre-Stirling numbers of the first kind.Several properties of the two new sequences are proved,such as the recurrence relations,vertical recurrence relation,forward difference.Also,this paper shows a relational expression of the Legendre-Stirling numbers of the extended first and second kinds.

关键词： generating functions Legendre-Stirling numbers of the first kind recurrence relations

作者: Fangqing Wen Haiyan Xie Xiangyu Jing Yangyang Li Fangyuan Hou

作者单位: Dept. of Mathematics, Dalian Maritime Uni, Dalian, China

会议类型: 国际会议

会议名称: 2016 2nd International Conference on Mechanical, Electronic and Information Technology Engineering(2016机械、电子和信息技术国际会议)

会议地点: 重庆

会议语种:英文

页码: 23-27

在线出版日期: 2016-03-21（万方平台首次上网日期，不代表论文的发表时间）