In the paper, by virtue of the binomial inversion formula, a general formula of higher order derivatives for a ratio of two differentiable function, and other techniques, the authors compute several sums in terms of the beta function and its partial derivatives, polygamma functions, the Gauss hypergeometric function, and a determinant. These results generalize known ones in combinatorics.

中文翻译：

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根据 beta、polygamma 和 Gauss 超几何函数计算总和

在论文中，作者借助二项式反演公式、两个可微函数之比的高阶导数通式等技术，计算了β函数及其偏导数、多伽马函数、高斯超几何函数和行列式。这些结果概括了组合学中已知的结果。