Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1990. Sectio Physicae (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 20)

Franczia Tamás: An arialytical inethod for calculating multicentre intégrais built up from GTF—S II.

- 4L — CB FCk) - J fCx) cos Ckx> dx C39a) o CD fCx) = I r FCk) cos Ckx) dk C39b> and TT J a CD FCk) = J fCx) sin Ckx) dx CdOa) o -2 b -M

2 * intC—oo :£ X £ +oo)expC-x

2) [cp- rx)

2+d

2l = J ' G * g „ dx L a L Cp— Tx) +d ] oo fCx) = j| J FCk) sin Ckx) dk C40b> equations o The integrability and the continuity of* fCx) and FCk> from 0 to +oo are the necessary conditions of the existence of the C39a3, C39b), C40a}, C40b) equations. Moreover C39a), C3Pb) demand the fCx)=fC—x) equality whereas C40a), C40b3 demand the fCx)="fC~x) one. If we want to calculate an integral of intC—oo ^ x Ü +<xOfCx,p} form by means of Fourier's cosinus— and sinus transforms with respect to p it is useful to express f Cx,p) as a sum of a gerade and an ungerade function of p: fCx,p) = f , Cx,p) + f r Cx,p) C41) ' * gCp) u 9 C p J f

gCp

3Cx,p)=CfCx,p)-»-fCx,-p)321,f

u9Cp

3Cx,p>=LfCx,p>-fCx,-p)32"

i C42a-b) + 00 + 00 +CO J f Cp, x)dx = S r

fl

C_,Cx,p3dx + S f (p)

C

x

fP

)dx Cd3

5 - CD -CD Y P -OO Y K First let us deal with the calculation of the first member in the right-side of C43). As f

g(j

3Cx,p) is a gerade function of p, intC—oo -K <, +oo)f , ^ Cx, p) is also a gerade function of p, because if FCp)=intCa ^ x £ b)fCx,p>, then FC-p)=intCa £ x £ b)fCx,~p) moreover in case of fCx,p)=fCx,-p) for each x and p FCp)=FC—p>

. Let «tCk) be equal to