Author(s)

T. Pham-Gia^1,2, Dinh Ngoc Thanh^2,3

¹Department of Mathematics and Statistics, Université de Moncton, Moncton, Canada.
²The Applied Multivariate Research Group, Université de Moncton, Moncton, Canada.
³Department of Mathematics and Computer Science, University of Science, Vietnam National University, Ho Chi Minh City, Vietnam.

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, Zonal Polynomial, Fractional Calculus, Lie Group, Cohomology, Computation

Pham-Gia, T. and Thanh, D. (2016) Hypergeometric Functions: From One Scalar Variable to Several Matrix Arguments, in Statistics and Beyond. Open Journal of Statistics, 6, 951-994. doi: 10.4236/ojs.2016.65078.