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Quantum Hilbert matrices and orthogonal polynomials

✍ Scribed by Jørgen Ellegaard Andersen; Christian Berg

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
436 KB
Volume
233
Category
Article
ISSN
0377-0427

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✦ Synopsis

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-

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.

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