用s-移位阶乘计算某些行列式
Calculation of some determinants using the s-shifted factorial
摘要：
几个决定因素与伽玛功能的元素进行评估。在计算随机矩阵的行列式的概率密度时会遇到这类行列式。s-移位阶乘被定义为幂函数、上升阶乘（或Pochammer符号）和下降阶乘的非负整数的推广。它是在组合理论中研究的二项式型多项式序列的特殊情况。在伽马函数方面，为负整数甚至复值定义了一个扩展。性质，主要是复合律和二项式公式。它们被用来评估家庭的广义范德蒙行列式的s-移位因子作为元素，而不是权力的功能。
英文摘要：
Several determinants with gamma functions as elements are evaluated. This kind of determinants are encountered in the computation of the probability density of the determinant of random matrices. The s-shifted factorial is defined as a generalization for non-negative integers of the power function, the rising factorial (or Pochammer's symbol) and the falling factorial. It is a special case of polynomial sequence of the binomial type studied in combinatorics theory. In terms of the gamma function, an extension is defined for negative integers and even complex values. Properties, mainly composition laws and binomial formulae, are given. They are used to evaluate families of generalized Vandermonde determinants with s-shifted factorials as elements, instead of power functions.
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