Tohoku Mathematical Journal

Quadratic relations for confluent hypergeometric functions

Hideyuki Majima, Kenji Matsumoto, and Nobuki Takayama

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Abstract

We present a theory of intersection on the complex projective line for homology and cohomology groups defined by connections which are regular or not. We apply this theory to confluent hypergeometric functions, and obtain, as an analogue of period relations, quadratic relations satisfied by confluent hypergeometric functions.

Article information

Source
Tohoku Math. J. (2) Volume 52, Number 4 (2000), 489-513.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178207752

Digital Object Identifier
doi:10.2748/tmj/1178207752

Mathematical Reviews number (MathSciNet)
MR2002e:32021

Zentralblatt MATH identifier
1006.33004

Subjects
Primary: 32G20: Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30]
Secondary: 33C15: Confluent hypergeometric functions, Whittaker functions, $_1F_1$ 33C60: Hypergeometric integrals and functions defined by them ($E$, $G$, $H$ and $I$ functions)

Keywords
Period relation confluent hypergeometric function intersection theory

Citation

Majima, Hideyuki; Matsumoto, Kenji; Takayama, Nobuki. Quadratic relations for confluent hypergeometric functions. Tohoku Math. J. (2) 52 (2000), no. 4, 489--513. doi:10.2748/tmj/1178207752. https://projecteuclid.org/euclid.tmj/1178207752


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