2007/03/19 by Jørgen Ellegaard Andersen, Jorgen Ellegaard Andersen, Christian Berg +2
Mathematics · Physics and Astronomy · #11B39 #33D45 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:11B39 #msc:33D45
paper · pdf · doi:10.48550/arxiv.math/0703546
10 pages
arxiv created 2007/03/19 · openalex publication_date 2007/03/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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-√(5))/(1+√(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.