Open Access
Translator Disclaimer
February 2009 Linear differential relations satisfied by Wirtinger integrals
Humihiko WATANABE
Hokkaido Math. J. 38(1): 83-95 (February 2009). DOI: 10.14492/hokmj/1248787013

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.

Citation

Download Citation

Humihiko WATANABE. "Linear differential relations satisfied by Wirtinger integrals." Hokkaido Math. J. 38 (1) 83 - 95, February 2009. https://doi.org/10.14492/hokmj/1248787013

Information

Published: February 2009
First available in Project Euclid: 28 July 2009

zbMATH: 1182.33011
MathSciNet: MR2501895
Digital Object Identifier: 10.14492/hokmj/1248787013

Subjects:
Primary: 33C05
Secondary: 14K25 , 34M45 , 55N25

Keywords: theta function , Wirtinger integral

Rights: Copyright © 2009 Hokkaido University, Department of Mathematics

JOURNAL ARTICLE
13 PAGES


SHARE
Vol.38 • No. 1 • February 2009
Back to Top