A Holonomic Ideal Annihilating the Fisher-Bingham Integral

Abstract

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.

arXiv comment11 pages

Cited by in corpus (3)

• The Holonomic Rank of the Fisher-Bingham System of Differential Equations
• Calculation of orthant probabilities by the holonomic gradient method
• Calculating the normalising constant of the Bingham distribution on the sphere using the holonomic gradient method