The holonomic rank of the Fisher–Bingham system of differential equations

The Fisher–Bingham system is a system of linear partial differential equations satisfied by the Fisher–Bingham integral for the n  -dimensional sphere SnSn. The system is given in [4, Theorem 2] and it is shown that it is a holonomic system [1]. We show that the holonomic rank of the system is equal to 2n+22n+2.