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
- 46 integral in (31). This integral can be calculated approximately with the method of the numerical analysis. In this case we ought to apply the Hermite-Gauss integration formula approaching the value of the integral with a sum. With this technique we could calculate the original • • d 3r CD integral applying the Hermite-Gauss-forrnula three times. But in this article we want to explain the beginning of an analytical method. In mathematics one of the methods for calculating definite real integrals is based upon the so-called residuum-theorem of the theory of complex variable functions. In some cases we can use a simpler form of this theorem, the Cauchy-theorem. Let us begin with showing the possibilities and the conditions of applying Cauchy's theorem for calculating definite real integrals. Let z = x +y=T-\ y = x+iy, where x,y are real numbers, x is the real part of z while iy is the imaginary one. Consisting of two parts z is called a complex number. The complex numbers can be described as the vectors of the complex Gauss-Argand number-plane:
