## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- 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

### Complex hypergeometric integrals

#### 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

**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