2016
DOI: 10.2206/kyushujm.70.315
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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

Abstract: 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 function… Show more

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Cited by 5 publications
(3 citation statements)
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References 20 publications
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“…( 7.26) can be written in terms of Appell F 2 functions. This is true, as shown for example in [55]. We now present a brief argument for why this must be the case.…”
Section: The Appell F 2 Functionmentioning
confidence: 74%
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“…( 7.26) can be written in terms of Appell F 2 functions. This is true, as shown for example in [55]. We now present a brief argument for why this must be the case.…”
Section: The Appell F 2 Functionmentioning
confidence: 74%
“…That this should be possible in the first place can be understood to be a consequence of the fact that each of the Appell functions can be defined by a particular system of linear differential equations (see section 7.3). A proof of this statement in twisted de Rham theory was given in [55] for the Lauricella functions F A , F B , F C , F D , which include the Appell functions as special cases, and for p+1 F p . A suitable choice of bases of forms and cycles will be discussed in each example in turn.…”
Section: Two-dimensional Integrals: Appell Functionsmentioning
confidence: 96%
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