Pfaffian Equations and Contiguity Relations of the Hypergeometric Function of Type (<i>k</i>+1, <i>k</i>+<i>n</i>+2) and Their Applications

DOI10.1619/fesi.61.315zbMath1426.33044arXiv1602.01637OpenAlexW2964323975MaRDI QIDQ5234841

Yoshiaki Goto, Keiji Matsumoto

Publication date: 4 October 2019

Published in: Funkcialaj Ekvacioj (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.01637

zbMATH Keywords

hypergeometric functionPfaffian equationcontiguity relationtwisted cohomology group

Mathematics Subject Classification ID

Other hypergeometric functions and integrals in several variables (33C70) Applications of hypergeometric functions (33C90)

Related Items (4)

Intersection numbers of twisted homology and cohomology groups associated to the Riemann–Wirtinger integral ⋮ Algorithms for Pfaffian Systems and Cohomology Intersection Numbers of Hypergeometric Integrals ⋮ AN ALGORITHM OF COMPUTING COHOMOLOGY INTERSECTION NUMBER OF HYPERGEOMETRIC INTEGRALS ⋮ Holonomic gradient method for two-way contingency tables

Uses Software

• hgm R

Cites Work

• Holonomic gradient descent and its application to the Fisher-Bingham integral
• Holonomic rank of \(\mathcal A\)-hypergeometric differential-difference equations
• Intersection numbers for logarithmic \(K\)-forms
• \(A\)-hypergeometric distributions and Newton polytopes
• Contiguity relations of Lauricella's \(F_D\) revisited
• MONODROMY AND PFAFFIAN OF LAURICELLA^|^apos;S FD IN TERMS OF THE INTERSECTION FORMS OF TWISTED (CO)HOMOLOGY GROUPS
• Gröbner basis and the problem of contiguous relations
• Theory of Hypergeometric Functions
• Contiguity Relations of Aomoto–Gel’fand Hypergeometric Functions and Applications to Appell’s System ${}_3 F_2 $ and Goursat’s System ${}_3 F_2 $
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