On Two Sequences of Orthogonal Polynomials Related to Jordan Blocks

被引：8

作者：

Capparelli, Stefano ^{[1
]}

Maroscia, Paolo ^{[1
]}

机构：

[1] Univ Roma La Sapienza, Dipartimento Sci Base & Applicate Ingn, I-00161 Rome, Italy

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2013年 / 10卷 / 04期

关键词：

Chebyshev polynomial; orthogonal polynomial; singular value; Catalan number; INTEGER COEFFICIENTS; CHEBYSHEV;

D O I：

10.1007/s00009-013-0283-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study two infinite sequences of polynomials related to Jordan blocks that have various interesting properties. We show that they are orthogonal polynomials whose sequences of moments are Catalan numbers and we relate them explicitly to the Chebyshev polynomials. We also use them to compute the singular values of some Jordan blocks. Finally, we investigate some combinatorial properties of the inverse sequences of these polynomials; we show them to be intimately related to the convolutions of the Catalan sequence.

引用

页码：1609 / 1630

页数：22

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