of the problem will have to be unknown for the present. 
The next step is to integrate equation (5.3). A few manipu- 
lations in the form of trigonometric identities and a transfor- 
mation of variable make it possible to put the equation into a 
form where the integral can be evaluated. The transformation of 
variable given by equation (5.4) and the formula for the sine of 
the sum of two angles yields equation (5.5). The trigonometric 
identity for the product of two sinusoidal terms can then be used 
to obtain equation (5.6). The assumption that n is an integer is 
used. 
Consider the first term in equation (5.6) (Plate X). The term 
under the integral can be expanded by the trigonometric identity 
for the sine of the sum of two angles and thus this integral can 
be written as the sum of two integrals. One of these integrals 
is given by equation (5.7). The integrand is an odd function, 
and the integral of an odd function from minus infinity to plus 
infinity is zero. The other term is even and its integral from 
minus infinity to plus infinity is equal to twice its integral 
from zero to infinity. The contribution of the first term is there- 
fore only the first term in equation (5.8). If this operation is 
carried out on each term in equation (5.6) the corresponding terms 
result in equation (5.8). 
The terms in equation (5.8) can be written as a double Fourier 
Integral by means of an interesting mathematical detour, and the 
double Fourier Integral can be evaluated by an interchange of the 
order of integration. The mathematics will be carried out for 
the first term in equation (5.8). 
= 0) < 
