Quantum Hilbert matrices and orthogonal polynomials

Details Quantum Hilbert matrices and orthogonal polynomials Quantum Hilbert matrices and orthogonal polynomials

2007-03-19

arxiv.org/abs/math/0703546v1

Mathematics

Classical Analysis and ODEs

10 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Quantum Hilbert matrices and orthogonal polynomials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quantum Hilbert matrices and orthogonal polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Hilbert matrices and orthogonal polynomials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-31718