Nakagiri's Monodromy Representations Associated with Appell's Hypergeometric Functions &lt;i&gt;F&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt; and &lt;i&gt;F&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;

Mimachi, Katsuhisa

doi:10.1619/fesi.60.77

Cited by 5 publications

(1 citation statement)

References 18 publications

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“…As for the expression of the circuit matrices in the cases of Gauss' 2 E 1 , Lauricella's E D , Jordan-Pochhammer's E J P and Appell's E 1 , E 2 , E 3 , we refer the reader to [MS1,MS2,MS3,M3].…”

Section: Introductionmentioning

confidence: 99%

ON A FUNDAMENTAL SET OF SOLUTIONS TO THE GENERALIZED HYPERGEOMETRIC EQUATION n+1En PRESENTED BY INTEGRALS OF EULER TYPE

Mimachi

2016

Kyushu J. Math.

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Abstract. We give a fundamental set of solutions to the generalized hypergeometric equation n+1 E n in terms of integrals of Euler type and explicitly determine the matrix elements of the circuit matrices with respect to this set of solutions. IntroductionThe generalized hypergeometric series n+1 F n is defined to be. It satisfies the generalized hypergeometric differential equation n+1 E n , which has regular singular points z = 0, 1, ∞ and whose rank is n + 1:where θ z = zd/dz and β n+1 = 1. The purpose of the present paper is to give a fundamental set of solutions of n+1 E n in terms of integrals of Euler type, and to express explicitly the matrix elements of the circuit matrices with respect to this set of solutions.We introduce some notation. When z is real and 0 < z < 1, let D j , j = 1, . . . , n + 1, be the domainof the real manifold (T z ) R , which is the real locus of

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Section: Introductionmentioning

confidence: 99%

ON A FUNDAMENTAL SET OF SOLUTIONS TO THE GENERALIZED HYPERGEOMETRIC EQUATION n+1En PRESENTED BY INTEGRALS OF EULER TYPE

Mimachi

2016

Kyushu J. Math.

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The Irreducibility of the Monodromy Representation Associated with the Dotsenko–Fateev Equation

Mimachi

2024

Commun. Math. Phys.

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Solutions in Terms of Integrals of Multivalued Functions for the Classical Hypergeometric Equations and the Hypergeometric System on the Configuration Space

Mimachi

Noumi

2016

Kyushu J. Math.

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Abstract. The systems of differential equations associated with the classical hypergeometric functions and the hypergeometric functions on the space of point configurations are investigated from the viewpoint of the twisted de Rham theory. In each case, it is proved that the integral of a certain multivalued function over an arbitrary twisted (or loaded) cycle satisfies the system of differential equations in question. The classical hypergeometric functions studied here include Appell's hypergeometric functions IntroductionIn this paper, we investigate the systems of differential equations associated with the classical hypergeometric functions, as well as the hypergeometric functions on the space of point configurations, in the framework of the twisted de Rham theory. In each case, we prove that the integral of a certain multivalued function over an arbitrary twisted (or loaded) cycle satisfies the system of differential equations in question. The classical hypergeometric functions studied here include Appell's hypergeometric functions F 1 , F 2 , F 3 , F 4 , Lauricella's hypergeometric functions F A , F B , F C , F D , and the generalized hypergeometric function n+1 F n . The corresponding differential equations will be denoted by E 1 , E 2 , E 3 , E 4 , E A , E B , E C , E D , and n+1 E n .We briefly explain the point of our investigation, taking the example of integrals associated with n+1 F n :

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Nakagiri's Monodromy Representations Associated with Appell's Hypergeometric Functions <i>F</i><sub>2</sub> and <i>F</i><sub>3</sub>

Cited by 5 publications

References 18 publications

ON A FUNDAMENTAL SET OF SOLUTIONS TO THE GENERALIZED HYPERGEOMETRIC EQUATION <b><i><sub>n</sub></i></b><b><sub>+</sub></b><sub>1</sub><b><i>E</i></b><b><i><sub>n </sub></i></b>PRESENTED BY INTEGRALS OF EULER TYPE

ON A FUNDAMENTAL SET OF SOLUTIONS TO THE GENERALIZED HYPERGEOMETRIC EQUATION <b><i><sub>n</sub></i></b><b><sub>+</sub></b><sub>1</sub><b><i>E</i></b><b><i><sub>n </sub></i></b>PRESENTED BY INTEGRALS OF EULER TYPE

The Irreducibility of the Monodromy Representation Associated with the Dotsenko–Fateev Equation

Solutions in Terms of Integrals of Multivalued Functions for the Classical Hypergeometric Equations and the Hypergeometric System on the Configuration Space

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