Hankel determinants of harmonic numbers and related topics
Johann Cigler
TL;DR
This paper reviews known results on Hilbert matrices, explores their connection with orthogonal polynomials, and computes Hankel determinants related to harmonic numbers, providing insights into their mathematical properties.
Contribution
It introduces new computations of Hankel determinants for harmonic numbers and discusses their relation to orthogonal polynomials and Hilbert matrices.
Findings
Computed explicit Hankel determinants for harmonic numbers
Connected Hankel determinants with orthogonal polynomial theory
Provided insights into properties of Hilbert matrices
Abstract
We give an overview of known results about Hilbert matrices from the point of view of orthogonal polynomials and compute Hankel determinants of harmonic numbers and related topics.
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Taxonomy
TopicsMathematical functions and polynomials · Advanced Mathematical Identities · Advanced Combinatorial Mathematics