The Holonomic Rank of the Fisher-Bingham System of Differential Equations

Tamio Koyama, Hiromasa Nakayama, Kenta Nishiyama, Nobuki Takayama

Published 2012-05-28, updated 2013-02-18Version 2

The Fisher-Bingham system is a system of linear partial differential equations satisfied by the Fisher-Bingham integral for the $n$-dimensional sphere $S^n$. The system is given in [Nakayama et al. (2011), Theorem 2] and it is shown that it is a holonomic system [Koyama]. We show that the holonomic rank of the system is equal to $2n+2$.