A Holonomic Ideal Annihilating the Fisher-Bingham Integral

Tamio Koyama

Published 2011-04-07, updated 2012-01-07Version 2

We calculate the integration ideal of annihilating differential operators of the non-normalized Fisher-Bingham distribution and show that the ideal agrees with the set of operators for the Fisher-Bingham integral given in "Holonomic Gradient Descent and its Application to the Fisher-Bingham Integral". They conjectured that the set generates a holonomic ideal and we prove their conjecture.