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

- 47 If Z

1

==

Xi

±

iy

i> Z2

=

X2

±i

y2' Lhe

n zx ± z2 = ^^^(yt^). zi • z2 = [

xi

+

iyJ- [

x2

+

1y

2] = = xi

x2

+i

xiy

2

+

iyi

x

2-yxy

2 = = [

xi

x

2-yiy

2] - i(

xty

a

+

xayi) according to the definitions of the summation and the multiplication of complex numbers. Let f(z) be a function of z projecting the complex number-plane onto itself. As the values of f(z) are complex numbers f(z) consists of a real and an imaginary part: fCz) = utx,y)+ivCx,y) , C32a) C32b) where u(x,y) and v(x,y) are real functions, b J fCz)dz means a complex integral of the f(z) function that must be a taken on the complex number-plane along the G curve between its a and b points: b b J fCz)dz = J ju(x,y)+ivCx,y}IdCx+xy) = a a L J C a 3 c o 3 b b = J [uCx,y)+ivCx

>

y)Jdx + f [uCx,y)+ivCx,y>JdCiy) =