On two sequences of orthogonal polynomials related to Jordan blocks. (English) Zbl 1279.33014
Mediterr. J. Math. 10, No. 4, 1609-1630 (2013); erratum ibid. 10, No. 4, 1613 (2013).
Summary: 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.
The erratum corrects a misprint in Proposition 3.1.
The erratum corrects a misprint in Proposition 3.1.
MSC:
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 11B65 | Binomial coefficients; factorials; \(q\)-identities |
| 05A15 | Exact enumeration problems, generating functions |
| 05E05 | Symmetric functions and generalizations |
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