Negative moments of orthogonal polynomials

被引：0

作者：

Jang, Jihyeug ^{[1
]}

Kim, Donghyun ^{[2
]}

Kim, Jang Soo ^{[1
]}

Song, Minho ^{[2
]}

Song, U-Keun ^{[1
]}

机构：

[1] Sungkyunkwan Univ, Dept Math, Suwon, South Korea

[2] Sungkyunkwan Univ, Appl Algebra & Optimizat Res Ctr, Suwon, South Korea

来源：

FORUM OF MATHEMATICS SIGMA | 2023年 / 11卷

基金：

新加坡国家研究基金会;

关键词：

05A15; 05A19; COMBINATORIAL; SHAPES;

D O I：

10.1017/fms.2023.23

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

If a sequence indexed by nonnegative integers satisfies a linear recurrence without constant terms, one can extend the indices of the sequence to negative integers using the recurrence. Recently, Cigler and Krattenthaler showed that the negative version of the number of bounded Dyck paths is the number of bounded alternating sequences. In this paper, we provide two methods to compute the negative versions of sequences related to moments of orthogonal polynomials. We give a combinatorial model for the negative version of the number of bounded Motzkin paths. We also prove two conjectures of Cigler and Krattenthaler on reciprocity between determinants.

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页数：34

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