000003302 001__ 3302
000003302 005__ 20190326205305.0
000003302 022__ $$a2314-4629
000003302 0247_ $$2DOI$$a10.1155/2019/6130464
000003302 037__ $$aARTICLE
000003302 041__ $$aeng
000003302 245__ $$aNon-integer valued winding numbers and a generalized residue theorem
000003302 260__ $$c2019-03
000003302 269__ $$a2019-03
000003302 300__ $$a9 p.
000003302 506__ $$avisible
000003302 520__ $$9eng$$aWe define a generalization of the winding number of a piecewise C1 cycle in the complex plane which has a geometric meaning also for points which lie on the cycle. The computation of this winding number relies on the Cauchy principal value but is also possible in a real version via an integral with bounded integrand. The new winding number allows to establish a generalized residue theorem which covers also the situation where singularities lie on the cycle. This residue theorem can be used to calculate the value of improper integrals for which the standard technique with the classical residue theorem does not apply.
000003302 540__ $$acorrect
000003302 592__ $$aHEIA-FR
000003302 592__ $$bAucun institut
000003302 592__ $$cIngénierie et Architecture
000003302 65017 $$aIngénierie
000003302 655__ $$ascientifique
000003302 700__ $$aHungerbühler, Norbert$$uDepartment of Mathematics, ETH Zürich, Zürich, Switzerland
000003302 700__ $$aWasem, Micha$$uSchool of Engineering and Architecture (HEIA-FR), HES-SO // University of Applied Sciences Western Switzerland
000003302 773__ $$g2019, vol. 2019$$tJournal of Mathematics
000003302 8564_ $$uhttps://hesso.tind.io/record/3302/files/Wasem_2019_non_integer_winding_numbers_residue_theorem.pdf$$s1665237
000003302 906__ $$aGOLD
000003302 909CO $$pGLOBAL_SET$$ooai:hesso.tind.io:3302
000003302 950__ $$aI2
000003302 981__ $$ascientifique
000003302 980__ $$ascientifique