Az Egri Ho Si Minh Tanárképző Főiskola Tud. Közleményei. 1987. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 18/13)

Tamás Franczia: An analytical method for calculating multicentre integrals built up from GTF-S I

- 48 b b b b J* uCx,y)dx+i J vCx,y>dx+i J" uCx,y)dy- J vCx,y)dy= CG) CG) u o = J juCx,y)dx-vCx, y)dyj+i J |uCx, y)dx+vCx, y)dxj , C34) where we have used (32a) and (32b). It is to be seen that a complex integral of a complex variable function can be calculated with the aid of real integrals. Let G be a closed curve of the complex number-plane and let f(z) be analytica

l on the set consisting of all points of the closed G curve and also in all points of the region of the plane bordered by this curve. In this case <£ fCz)dz = 0. C GD C35) This is Cauchy's theorem. The analytic

y of f(z) on a set means that f Cz) lim h —* O fCz+h)-f(z) v* + C3Ó) exists in each point of the set, where h means complex numbers. The operation defined in (36) is called the complex derivation of f(z).