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arXiv · 2608.18670

A general method of deducing the determinantal expressions for polynomial and its derivative

Hongyi Lou·Shi-Mei Ma·Xinzhe Song·Guiying Yan·Yeong-Nan Yeh
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Abstract

In this paper, we present a general method of deducing the determinantal expressions for a polynomial and its derivative. As illustrations, we provide three determinantal expressions for the derivative of the Eulerian polynomial. Using a functional equation discovered by Gessel,we also establish the determinantal expressions for the second-order Eulerian polynomial and its derivative.

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Hongyi Lou, Shi-Mei Ma, Xinzhe Song, Guiying Yan, Yeong-Nan Yeh. 2026-08-19. A general method of deducing the determinantal expressions for polynomial and its derivative. https://arxiv.org/abs/2608.18670

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