Contiguity relations of Lauricella's F_D revisited

2014/12/10 by Yoshiaki Gotō, Goto, Yoshiaki · 2 citations
Computer Science · Engineering · Physics and Astronomy · #33C65 #33C90 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1412.3256

openalex publication_date 2014/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study contiguity relations of Lauricella's hypergeometric function F_D, by using the twisted cohomology group and the intersection form. We derive contiguity relations from those in the twisted cohomology group and give the coefficients in these relations by the intersection numbers. Furthermore, we construct twisted cycles corresponding to a fundamental set of solutions to the system of differential equations satisfied by F_D, which are expressed as Laurent series. We also give the contiguity relations of these solutions.

Cited by

• A-Hypergeometric Distributions and Newton Polytopes
• Pfaffian Systems of A-Hypergeometric Systems II --- Holonomic Gradient Method

Related

• Twisted period relations for Lauricella's hypergeometric function F_A
• Relative twisted homology and cohomology groups associated with Lauricella's F_D
• Pfaffian of Lauricella's hypergeometric system F_A
• The monodromy representation of Lauricella's hypergeometric function F_C
• Intersection numbers and twisted period relations for the generalized hypergeometric function _m+1 F_m