TY - JOUR
T1 - The Jacobi-Stirling numbers
AU - Andrews, George E.
AU - Egge, Eric S.
AU - Gawronski, Wolfgang
AU - Littlejohn, Lance L.
N1 - Funding Information:
E-mail addresses: andrews@math.psu.edu (G.E. Andrews), eegge@carleton.edu (E.S. Egge), gawron@uni-trier.de (W. Gawronski), Lance_Littlejohn@baylor.edu (L.L. Littlejohn). 1 The first author is partially supported by National Security Agency Grant H98230-12-1-0205.
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jcta.2012.08.006
DO - 10.1016/j.jcta.2012.08.006
M3 - Article
AN - SCOPUS:84865435686
SN - 0097-3165
VL - 120
SP - 288
EP - 303
JO - Journal of Combinatorial Theory. Series A
JF - Journal of Combinatorial Theory. Series A
IS - 1
ER -