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

- 49 Cauchy and Riemann have proved that f'(z) exists in the z point only in 111 . r. •• <?

U ÖV that case if the cTy> partial derivatives exist in this point and satisfy the so-called Cauchy-Riemann equations: How can we calculate/ fCx^dxusing Cauchy's theorem? First we have to write z in place of x in f(x) then we have to form the fCz)dzintegral along a closed G curve containing the ta,b] interval of the x-axis. If f(z) is analytical along G and within the region of the plane bordered by G we-can write using (35) and the z=x,if y=0 equation: § fCz)dz = J fCz)dz + J fCz)dz + . . . + J fCz)dz + _ dy <3u Cx C)y ' cjy d\i _ Öv rn'y^ ~ cK C37;

> b CL b z + J fCx)dx + . . . + J fCzDdz = O n C38} z n-1 CG where G.UG

2U ... UA

ku ... uta,bi u ... ua n - 1 Q. (U is the sign of forming the union of sets.) If we can calculate the values of the integrals of the sum in the