The explicit formula of Hankel determinant with Catalan elements
Jishe Feng
TL;DR
This paper derives an explicit formula for Hankel determinants with Catalan elements using simplified binomial coefficient determinant formulas, presenting new results in this area.
Contribution
It introduces a new explicit formula for Hankel determinants with Catalan elements, simplifying previous complex expressions.
Findings
Explicit formula for Hankel determinants with Catalan elements
Simplification of previous determinant formulas
New results in combinatorial matrix analysis
Abstract
Applying Johann Cigler's Hankel determinant formula in terms of the binomial coefficient determinants, which is simplified from Christian Krattenthale's, we get an explicit formula of Hankel determinants for general. As far as I know, those are new results.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Advanced Mathematical Theories and Applications