推导多项式及其行列式表达式的通用方法
A general method of deducing the determinantal expressions for polynomial and its derivative
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中文总结 AI 辅助
该研究提出推导多项式及其导数行列式表达式的通用方法，以欧拉多项式为例给出相关行列式表达式，利用Gessel的函数方程建立二阶欧拉多项式及其导数的行列式表达式。
中文摘要 AI 辅助
本文提出一种推导多项式及其导数的行列式表达式的通用方法。作为示例，给出了欧拉多项式导数的三个行列式表达式；利用Gessel发现的函数方程，还建立了二阶欧拉多项式及其导数的行列式表达式。
英文摘要
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.
