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2017•International Journal of MathematicsRequires access

A system of hypergeometric differential equations in two variables of rank 9

Jyoichi Kaneko, Keiji Matsumoto, Katsuyoshi Ohara

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Abstract

We study a hypergeometric function in two variables and a system of hypergeometric differential equations associated with this function. This is a regular holonomic system of rank [Formula: see text]. We give a fundamental system of solutions to this system in terms of this hypergeometric series. We give circuit matrices along generators of the fundamental group of the complement of its singular locus with respect to our fundamental system.

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What this paper is about

We study a hypergeometric function in two variables and a system of hypergeometric differential equations associated with this function. This is a regular holonomic system of rank [Formula: see text]. We give a fundamental system of solutions to this system in terms of this hypergeometric series. We give circuit matrices along generators of the fundamental group of the complement of its singular locus with respect to our fundamental system.

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OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We study a hypergeometric function in two variables and a system of hypergeometric differential equations associated with this function. This is a regular holonomic system of rank [Formula: see text]. We give a fundamental system of solutions to this system in terms of this hypergeometric series. We give circuit matrices along generators of the fundamental group of the complement of its singular locus with respect to our fundamental system.

Key concepts: Mathematics, Hypergeometric distribution, Rank (graph theory), Hypergeometric function, Appell series, Differential (mechanical device), Frobenius solution to the hypergeometric equation, Confluent hypergeometric function

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