558 
: : : ; ly 
This residue is the coefficient of Fu in 
eae (GO = C=) (Noch), Ln da) 
i= : 
Now 
(a) 
JB 2 152 di 
lg (le) =lge — bed af at 
1 ry in 
2/2 4/4 !6 
as may be shown by integrating 
1 ee. B B TB 
- = 1 12 Sc =< P=, mod z Qa 
Pi 7 Aj Th Beh 6 IE 
where 
B =t, B, = zh B, =d 
between the limits o and z 
Substituting the values of lg (l—e%), we obtain 
Be IBS, 0 
1 vt = 
= 6 Wp Be onl 42 
2 
a,4,-..4,¢ 
where 
pnt ds and s;—af Haf 4... af 
hence W, is the coefficient of #—*t in the product 
1 
1 ( 1 1 1 
el | DÛ de =D DP de pe ie Ae 
ANRA u 2 T By 2 Tp ig 
1 t? : 
(1-3 ker a 
fy te cae EE 
2880 
Applying the preceding to compute the number of solutions of 
the equation 
2, toer, + 102, + 20e, ==. 
we first observe that the different divisors of 1, 2, 5, 10, 20 are 
ard Uc OMEN Vesa nino be enone 
wv 
5, 4 
10, 5 
10 
20 
thus 
D («) = (le) (la)? (Le) (le)? (1 — a7")? (Lr?) 
