Hankel determinants of linear combinations of moments of orthogonal polynomials. II

DOI10.1007/s11139-021-00514-8arXiv2101.04225OpenAlexW3215675858MaRDI QIDQ6098230

Christian Krattenthaler

Publication date: 13 June 2023

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.04225

zbMATH Keywords

Chebyshev polynomialsHankel determinantsCatalan numbersMotzkin numbersSchröder numbersDelannoy numbersRiordan numberscentral binomial coefficientsmoments of orthogonal polynomialsDodgson condensationfine numberscentral trinomial numbers

Mathematics Subject Classification ID

Umbral calculus (05A40) Exact enumeration problems, generating functions (05A15) Determinants, permanents, traces, other special matrix functions (15A15) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Random matrices (algebraic aspects) (15B52) Relations with random matrices (11M50) Matrices, determinants in number theory (11C20) Toeplitz, Cauchy, and related matrices (15B05)

Cites Work

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• A unified approach for the Hankel determinants of classical combinatorial numbers
• Determinants of (generalised) Catalan numbers
• Advanced determinant calculus
• Hankel determinants of linear combinations of consecutive Catalan-like numbers
• Products and ratios of characteristic polynomials of random Hermitian matrices
• Hankel determinants of linear combinations of moments of orthogonal polynomials
• Characteristic polynomials of random matrices.

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