2017
DOI: 10.1619/fesi.60.77
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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>

Abstract: Abstract. We study monodromy representations associated with Appell's hypergeometric functions F 2 and F 3 by using integrals of multivalued functions. In particular, we derive Nakagiri's matix elements of the representations in a di¤erent manner and relax his conditions on the parameters. As an application, we give a simple and elementary derivation of su‰cient conditions that the systems of di¤erential equations satisfied by F 2 and F 3 are irreducible.

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Cited by 5 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%
“…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%