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
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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