Abstract
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 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 language | English |
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Journal | Journal of Computational and Applied Mathematics |
Volume | 233 |
Issue number | 3 |
Pages (from-to) | 723-729 |
Number of pages | 7 |
ISSN | 0377-0427 |
DOIs | |
Publication status | Published - 2009 |
Externally published | Yes |