2022-08-18T02:16:55Zhttps://kitami-it.repo.nii.ac.jp/oaioai:kitami-it.repo.nii.ac.jp:000081892022-03-15T07:21:05Z1:87Linear differential relations satisfied by Wirtinger integralsWATANABE, Humihikoopen accessc2009 Hokkaido University, Department of MathematicsWirtinger integraltheta functionWe will derive linear differential relations satisfied by Wirtinger integrals\nby exploiting classical formulas of Jacobi’s theta functions. Although Wirtinger integrals\nare related to Gauss’ hypergeometric functions, we will do that without referring\nto Gauss’ hypergeometric differential equation. We believe that our method to derive\nthem will be applicable to another definite integral defined on the torus which has as\nintegrand a power product of not necessarily four theta functions, and which is not a\nlift of any definite integral defined on the complex projective line.Hokkaido University, Department of Mathematics2007engjournal articleVoRhttps://kitami-it.repo.nii.ac.jp/records/8189Hokkaido Math. J.388395https://kitami-it.repo.nii.ac.jp/record/8189/files/2009_Linear differential relations satisfied by Wirtinger integrals.pdfapplication/pdf209.3 kB2016-11-22