TITLE:
Hypergeometric Functions: From One Scalar Variable to Several Matrix Arguments, in Statistics and Beyond
AUTHORS:
T. Pham-Gia, Dinh Ngoc Thanh
KEYWORDS:
Hypergeometric, Zonal Polynomial, Fractional Calculus, Lie Group, Cohomology, Computation
JOURNAL NAME:
Open Journal of Statistics,
Vol.6 No.5,
October
27,
2016
ABSTRACT: 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.