Work

Linear differential relations satisfied by Wirtinger integrals

Year: 2009

Type: article

Abstract: We will derive linear differential relations satisfied by Wirtinger integrals by exploiting classical formulas of Jacobi’s theta functions. Although Wirtinger integrals are related to Gauss' hypergeometric functions, we will do that without referring to Gauss' hypergeometric differential equation. We believe that our method to derive them will be applicable to another definite integral defined on the torus which has as integrand a power product of not necessarily four theta functions, and which is not a lift of any definite integral defined on the complex projective line.

Source: Hokkaido Mathematical Journal

DOI: 10.14492/hokmj/1248787013

Author: Humihiko WATANABE

Institution: Kitami Institute of Technology

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Japan Society for the Promotion of Science

Award: Study on a new generalization of the hypergeometric integral via modular property