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Transactions of the American Mathematical Society

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Confluence of cycles
for hypergeometric functions on $Z_{2,n+1}$


Author: Yoshishige Haraoka
Journal: Trans. Amer. Math. Soc. 349 (1997), 675-712
MSC (1991): Primary 33C60, 33C65, 33C70
DOI: https://doi.org/10.1090/S0002-9947-97-01471-2
MathSciNet review: 1321577
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Abstract: The hypergeometric function of general type, which is a generalization of the classical confluent hypergeometric functions, admits an integral representation derived from a character of a linear abelian group. For the hypergeometric function on the space of $2\times (n+1)$ matrices, a basis of cycles for the integral is constructed by a limit process, which is called a process of confluence. The determinant of the period matrix is explicitly evaluated to show the independence of the cycles.


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Additional Information

Yoshishige Haraoka
Affiliation: Department of Mathematics, Faculty of General Education, Kumamoto University, Kumamoto 860, Japan
Email: haraoka@gpo.kumamoto-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-97-01471-2
Keywords: Confluent hypergeometric function, twisted homology, confluence, period matrix
Received by editor(s): July 28, 1994
Received by editor(s) in revised form: January 9, 1995
Additional Notes: Partially supported by Grant-in-Aid for Encouragement of Young Scientists (No. 05740105), the Ministry of Education, Science and Culture, Japan
Article copyright: © Copyright 1997 American Mathematical Society

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