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

Haraoka, Yoshishige

doi:10.1090/S0002-9947-97-01471-2

Confluence of cycles for hypergeometric functions on $Z_{2,n+1}$
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Trans. Amer. Math. Soc. 349 (1997), 675-712 Request permission

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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