Nobuki TAKAYAMA 
Nobuki TAKAYAMA
Department of Mathematics,
Graduate School of Science, Kobe University 
Division : Applied Mathematics
Professor 
Building B, Room 320
Personal Website

Research Field :
Hypergeometric Functions, Computer Algebra (algorithms, applications, and implementations)


Research Summary :
In the last 5 years, I have studied applications of hypergeometric functions
of several variables to statistics.
The main topic has been the holonomic gradient method
( HGM ),
which is a method to evaluate numerically normalizing constants and
their derivatives of "holonomic" probability distributions.
The theory and algorithms for hypergeometric functions are used for evaluations.


Primary Publications : 

T.Hibi et al, Groebner Bases : Statistics and Software Systems , Springer, 2013.
 Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
Holonomic gradient method for the distribution function of the largest root of a Wishart matrix
Journal of Multivariate Analysis,
117 (2013)
296312 .

Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
Tomonari Sei, Nobuki Takayama, Akimichi Takemura,
Holonomic Gradient Descent and its Application to FisherBingham Integral
Advances in Applied Mathematics 47 (2011),
639658.


