The purpose of the present paper is to give unified expressions to the characteristic functions of all elliptical and related distributions. Those distributions including the multivariate elliptical symmetric distributions and some asymmetric distributions such as skew-elliptical distributions and their location-scale mixtures. In particular, we get simple closed form of characteristic functions for important cases such as the multivariate Student-$t$, Cauchy, logistic, Laplace, symmetric stable. The expressions of characteristic functions involve Bessel type functions or generalized hypergeometric series.

翻译：本文旨在给出所有椭圆分布及相关分布的特征函数的统一表达式。这些分布包括多元椭圆对称分布以及某些非对称分布，如偏椭圆分布及其位置-尺度混合分布。特别地，我们针对多元学生t分布、柯西分布、逻辑分布、拉普拉斯分布、对称稳定分布等重要情形，得到了特征函数的简洁闭式。特征函数的表达式涉及贝塞尔型函数或广义超几何级数。