交错Zeta函数的一种新的概率表示和一种新的Selberg型积分计算
A New Probabilistic Representation of the Alternating Zeta Function and a New Selberg-like Integral Evaluation
摘要：
本文给出了交错Zeta函数的两种新表示。我们表明，对于任何s $\in$ C这个功能可以计算为一系列的行列式的限制。然后我们将这些行列式表示为具有Dixon-Anderson密度的随机向量的泛函的期望。将这种表示推广到更一般的交错级数，使我们能够用广义范德蒙德行列式计算Selberg型积分。
英文摘要：
In this paper, we present two new representations of the alternating Zeta function. We show that for any s $\in$ C this function can be computed as a limit of a series of determinant. We then express these determinants as the expectation of a functional of a random vector with Dixon-Anderson density. The generalization of this representation to more general alternating series allows us to evaluate a Selberg-type integral with a generalized Vandermonde determinant.
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