Hypergeometric Functions: From One Scalar Variable to Several Matrix Arguments, in Statistics and Beyond  

作　　者：T. Pham-Gia Dinh Ngoc Thanh T. Pham-Gia;Dinh Ngoc Thanh(Department of Mathematics and Statistics, Université de Moncton, Moncton, Canada;The Applied Multivariate Research Group, Université de Moncton, Moncton, Canada;Department of Mathematics and Computer Science, University of Science, Vietnam National University, Ho Chi Minh City, Vietnam)

机构地区：[1]Department of Mathematics and Statistics, Université de Moncton, Moncton, Canada [2]The Applied Multivariate Research Group, Université de Moncton, Moncton, Canada [3]Department of Mathematics and Computer Science, University of Science, Vietnam National University, Ho Chi Minh City, Vietnam

出　　处：《Open Journal of Statistics》2016年第5期951-994,共45页统计学期刊（英文）

摘　　要：Hypergeometric functions have been increasingly present in several disciplines including Statistics, but there is much confusion on their proper uses, as well as on their existence and domain of definition. In this article, we try to clarify several points and give a general overview of the topic, going from the univariate case to the matrix case, in one and then in several arguments. We also survey some results in fields close to Statistics, where hypergeometric functions are actively used, studied and developed.Hypergeometric functions have been increasingly present in several disciplines including Statistics, but there is much confusion on their proper uses, as well as on their existence and domain of definition. In this article, we try to clarify several points and give a general overview of the topic, going from the univariate case to the matrix case, in one and then in several arguments. We also survey some results in fields close to Statistics, where hypergeometric functions are actively used, studied and developed.

关 键 词：HYPERGEOMETRIC Zonal Polynomial Fractional Calculus Lie Group COHOMOLOGY Computation 

分 类 号：O17[理学—数学]