Abstract In the paper, employing methods and techniques in analysis and linear algebra, the authors find a simple formula for computing an interesting Hessenberg determinant whose elements are products of binomial coefficients and falling factorials, derive explicit formulas for computing some special Hessenberg and tridiagonal determinants, and alternatively and simply recover some known results.

中文翻译：

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几个 Hessenberg 行列式的计算

摘要 在论文中，作者利用分析和线性代数中的方法和技术，找到了一个简单的公式来计算一个有趣的 Hessenberg 行列式，其元素是二项式系数和降阶乘的乘积，推导出一些特殊的 Hessenberg 行列式和三对角行列式的显式公式，或者简单地恢复一些已知的结果。