Multiple Laguerre polynomials: Combinatorial model and Stieltjes moment representation

Abstract

I give a combinatorial interpretation of the multiple Laguerre polynomials of the first kind of type II, generalizing the digraph model found by Foata and Strehl for the ordinary Laguerre polynomials. I also give an explicit integral representation for these polynomials, which shows that they form a multidimensional Stieltjes moment sequence whenever $x\le 0$.

LaTeX2e, 11 pages. Version 2 fixes Remark 2 on page 5. To be published in Proceedings of the AMS

References in corpus (2)

• Multiple orthogonal polynomials, $d$-orthogonal polynomials, production matrices, and branched continued fractions
• Lattice paths and branched continued fractions. III. Generalizations of the Laguerre, rook and Lah polynomials

Cited by in corpus (2)

• When does a hypergeometric function ${}_p{F}_q$ belong to the Laguerre--Pólya class $L{P}^{+}$?
• Continued fractions using a Laguerre digraph interpretation of the Foata--Zeilberger bijection and its variants