Quantum Hilbert matrices and orthogonal polynomials

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dc.creatorAndersen, Jorgen Ellegaard
dc.creatorBerg, Christian
dc.date2007-03-19
dc.date.accessioned2026-07-07T07:52:37Z
dc.date.available2026-07-07T07:52:37Z
dc.descriptionUsing the notion of quantum integers associated with a complex number $q\neq 0$, we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little $q$-Jacobi polynomials when $|q|<1$, and for the special value $q=(1-\sqrt{5})/(1+\sqrt{5})$ they are closely related to Hankel matrices of reciprocal Fibonacci numbers called Filbert matrices. We find a formula for the entries of the inverse quantum Hilbert matrix.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0703546
dc.identifierhttp://arxiv.org/abs/math/0703546
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125946
dc.subjectClassical Analysis and ODEs
dc.subject33D45;11B39
dc.titleQuantum Hilbert matrices and orthogonal polynomials
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