Then, forn =AtT1 
an 
| cos”***(g- go Jag = 
(0) 
i cos?” (g-go )sin(Q-o i 
eT 
TE | cos (p-go lag 
= aaa [cos**(21-go0 )sin(2T7-Zo )+cos? "go sino ] 
hii 
| cos?*-*g-p )dg = 0 
(©) 
2k 
2hF1 
+ 
since 
T 
2, 
' cos?*"1(g-Go dg = 0 
by induction hypothesis. In a like manner the other integrals 
are evaluated. 
Since the integrals involved often contain Bessel functions 
in the integrand, or some other function that must be 
expanded in an infinite series in order to evaluate the 
integrals, two conditions must be satisfied before the 
integral can be evaluated: 
1. The infinite series must be uniformly convergent, and the 
individual terms must be continuous. 
2. The limits of integration must be within the interval of 
convergence of the series. 
All the integrands treated in this report satisfy these con- 
ditions when term-by-term integration is employed. 
Furthermore, if the series is an alternating series that 
is monotone nonincreasing, that is uniformly convergent 
on its interval of convergence, then the error after trun- 
cating the series after n terms is majorized by the magnitude 
of the (n+1)th term. This is a convenient method of judging 
the error. 
45 
