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

2012/05/28 by Tamio Koyama, Koyama, Tamio, Hiromasa Nakayama +5
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Quantum Algebra (math.QA) #math.CA #math.QA

paper · pdf · doi:10.48550/arxiv.1205.6144

15 pages

arxiv created 2013/02/18 · arxiv updated 2013/02/19

Abstract

The Fisher-Bingham system is a system of linear partial differential equations satisfied by the Fisher-Bingham integral for the n-dimensional sphere Sⁿ. 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.

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