Advanced Studies in Pure Mathematics

Complex hypergeometric integrals

Katsuhisa Mimachi

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Abstract

We consider a complex version of the Gauss hypergeometric integral from the view point of the twisted de Rham theory. In particular, we give a formula to express the complex hypergeometric integral in terms of the hermitian form of the ordinary Gauss hypergeometric integrals.

Article information

Source
Representation Theory, Special Functions and Painlevé Equations — RIMS 2015, H. Konno, H. Sakai, J. Shiraishi, T. Suzuki and Y. Yamada, eds. (Tokyo: Mathematical Society of Japan, 2018), 469-485

Dates
Received: 16 March 2016
First available in Project Euclid: 21 September 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1537499434

Digital Object Identifier
doi:10.2969/aspm/07610469

Mathematical Reviews number (MathSciNet)
MR3837930

Zentralblatt MATH identifier
07039311

Subjects
Primary: 33C60: Hypergeometric integrals and functions defined by them ($E$, $G$, $H$ and $I$ functions)
Secondary: 33B15: Gamma, beta and polygamma functions 33C15: Confluent hypergeometric functions, Whittaker functions, $_1F_1$

Keywords
complex hypergeometric integrals complex beta integrals twisted de Rham theory

Citation

Mimachi, Katsuhisa. Complex hypergeometric integrals. Representation Theory, Special Functions and Painlevé Equations — RIMS 2015, 469--485, Mathematical Society of Japan, Tokyo, Japan, 2018. doi:10.2969/aspm/07610469. https://projecteuclid.org/euclid.aspm/1537499434


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