( 496 ) 
Let us now determine the integral of this equation satisfying the 
conditions that for « — 0 
5 cos? pd wy ld 
Ui = 
1—2# cos? pt (lt) 
0 
and 
du 
da 
We then find 
a 
7 mz — mz J Fk ne ne 
= aes ae +e fa = a ‘| (9) dp |e oe) aes e Kf) 
4 (1l—t®) 8 t° m B 
0 
and by this 
Er t ! ra 7 ] 
hee =e ea ie 
1.3 4 0 
sk 1 ) dm 1 
a er (5) 1 2 1 9 ‘--) : 
+ +f 3 dp Sie Ë —e 
0 
Remembering now that 
ag) 
ae =D HtLD HELD H.. 
il 1 
mn 0/0 
we see that the residues are easily determined. We have 
Sn In () In (0) = TUe Le +o] + 
« (2,8) 
+ $f SUG et ete. 0 
0 
From this result another important relation may be deduced. To 
show this, we shall again develop 
Le —ea) + L(e +e) 
into a series. 
From 
1 7 
Ie) = { sin p sin (x sin p — asin p) dy 
wT 
0 
and 
