Tohoku Mathematical Journal

Quadratic relations for confluent hypergeometric functions

Hideyuki Majima, Kenji Matsumoto, and Nobuki Takayama

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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.

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

First available in Project Euclid: 3 May 2007

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Zentralblatt MATH identifier

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)

Period relation confluent hypergeometric function intersection theory


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.

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