SOLUTIONS IN TERMS OF INTEGRALS OF MULTIVALUED FUNCTIONS FOR THE CLASSICAL HYPERGEOMETRIC EQUATIONS AND THE HYPERGEOMETRIC SYSTEM ON THE CONFIGURATION SPACE

作者：Mimachi Katsuhisa^*; Noumi Masatoshi

来源：Kyushu Journal of Mathematics, 2016, 70(2): 315-342.

DOI：10.2206/kyushujm.70.315

• hypergeometric integrals
• classical hypergeometric equations
• classical hypergeometric functions
• Appell's hypergeometric functions F-1, F-2, F-3, F-4
• Lauricella's hypergeometric functions F-A, F-B, F-C, F-D
• generalized hypergeometric function F-n+1(n)
• hypergeometric function on the configuration space

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 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 F-n+1(n).

• 出版日期2016-9