The Jacobi-Stirling numbers

被引：27

作者：

Andrews, George E. ^{[1
]}

Egge, Eric S. ^{[2
]}

Gawronski, Wolfgang ^{[3
]}

Littlejohn, Lance L. ^{[4
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16801 USA

[2] Carleton Coll, Dept Math, Northfield, MN 55057 USA

[3] Univ Trier, Dept Math, D-54286 Trier, Germany

[4] Baylor Univ, Dept Math, Waco, TX 76798 USA

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2013年 / 120卷 / 01期

关键词：

Jacobi-Stirling numbers; Legendre-Stirling numbers; Stirling numbers; Jacobi polynomials; Left-definite theory;

D O I：

10.1016/j.jcta.2012.08.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Jacobi-Stirling numbers were discovered as a result of a problem involving the spectral theory of powers of the classical second-order Jacobi differential expression. Specifically, these numbers are the coefficients of integral composite powers of the Jacobi expression in Lagrangian symmetric form. Quite remarkably, they share many properties with the classical Stirling numbers of the second kind which are the coefficients of integral powers of the Laguerre differential expression. In this paper, we establish several properties of the Jacobi-Stirling numbers and its companions including combinatorial interpretations, thereby extending and supplementing known recent contributions to the literature. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：288 / 303

页数：16

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