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arXiv · 2503.17187

Hankel Determinants for Convolution of Power Series: An Extension of Cigler's Results

Feihu Liu·Ying Wang·Yingrui Zhang·Zihao Zhang
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Abstract

Cigler considered certain shifted Hankel determinants of convolution powers of Catalan numbers and conjectured identities for these determinants. Recently, Fulmek gave a bijective proof of Cigler's conjecture. Cigler then provided a computational proof. We extend Cigler's determinant identities to the convolution of general power series $F(x)$, where $F(x)$ satisfies a certain type of quadratic equation. As an application, we present the Hankel determinant identities of convolution powers of Motzkin numbers.

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Feihu Liu, Ying Wang, Yingrui Zhang, Zihao Zhang. 2025-03-21. Hankel Determinants for Convolution of Power Series: An Extension of Cigler's Results. https://arxiv.org/abs/2503.17187

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