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Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas ( IF 1.8 ) Pub Date : 2020-08-24 , DOI: 10.1007/s13398-020-00927-y Feng Qi 1, 2, 3 , Chuan-Jun Huang 4
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas ( IF 1.8 ) Pub Date : 2020-08-24 , DOI: 10.1007/s13398-020-00927-y Feng Qi 1, 2, 3 , Chuan-Jun Huang 4
Affiliation
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:
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。
更新日期:2020-08-24
中文翻译:
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。