Quantum Hilbert matrices and orthogonal polynomials

[摘要] Using the notion of quantum integers associated with a complex number n not equal 0, we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q-Jacobi polynomials when vertical bar q vertical bar < 1, and for the special value q = (1-root 5)/(1+root 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. (C) 2009 Elsevier B.V. All rights reserved.

[发布日期] 2009-12-01

[效力级别]  Proceedings Paper

[关键词] Basic orthogonal polynomials;Quantum integers;Fibonacci numbers