Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions

Feng Qi1,2,3, Chuan-Jun Huang4
1Institute of Mathematics, Henan Polytechnic University, Jiaozuo, China
2College of Mathematics and Physics, Inner Mongolia University for Nationalities, Tongliao, China
3School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin, China
4Department of Mathematics, Ganzhou Teachers College, Ganzhou, China

Tóm tắt

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.

Tài liệu tham khảo

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