Quantum Hilbert matrices and orthogonal polynomials

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Using 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.
10 pages

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Classical Analysis and ODEs, 33D45;11B39

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http://salesiana.dossiersoluciones.com/handle/123456789/125946

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0703546
 http://arxiv.org/abs/math/0703546

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arXiv