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Quantum Hilbert matrices and orthogonal polynomials

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  • Jørgen Ellegaard Andersen, Denmark
  • Christian Berg, Denmark
Using the notion of quantum integers associated with a complex number q≠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 View the MathML source 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.
Original languageEnglish
JournalJournal of Computational and Applied Mathematics
Pages (from-to)723-729
Number of pages7
Publication statusPublished - 2009

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