论文信息 - Quantum Hilbert matrices and orthogonal polynomials

Quantum Hilbert matrices and orthogonal polynomials

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 q=(1-5)(1+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.

Christian Berg | Jørgen Ellegaard Andersen | C. Berg | J. Andersen

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