A Holonomic Ideal Annihilating the Fisher-Bingham Integral

2011/04/07 by Tamio Koyama, Koyama, Tamio
Economics, Econometrics and Finance · Mathematics · #16F10 #16S32 #16Z99 #32C38 #33F10 #66H11 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Random Matrices and Applications #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1104.1411

openalex publication_date 2011/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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