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Duality for hypergeometric functions and invariant Gauss-Manin systems

Published online by Cambridge University Press:  04 December 2007

MICHITAKE KITA  and
KEIJI MATSUMOTO
MICHITAKE KITA
Affiliation:
Department of Mathematics, College of Liberal Arts, Kanazawa University, Kakuma Kanazawa 920-11, Japan
KEIJI MATSUMOTO
Affiliation:
Department of Mathematics, Faculty of Science, Hiroshima University, Kagamiyama Higashi-Hiroshima 739, Japan; e-mail: matsu@knight.math.schi.hiroshima-u.ac.jp
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Abstract

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We present some basic identities for hypergeometric functions associated with the integrals of Euler type. We give a geometrical proof for formulae such as the identity between the single and double integrals expressing Appell's hypergeometric series $F_1 (a, b, b^{\prime} c; x, y)$.

Keywords

hypergeometric functiontwisted (co)homology groupGauss-Manin connectionperiod matrix
Type
Research Article
Information
Compositio Mathematica , Volume 108 , Issue 1 , August 1997 , pp. 77 - 106
Copyright
© 1997 Kluwer Academic Publishers