560 
hence 
o-” ent t 
i, = Sy <= 
(1— ge~')(1 —9%e—*')(1—o%e 5')(1 —e*%e—101) (1 9?%e~ 204 ((¢)) 
where the summation must be extended to both the roots o of 
N 
the equation 1+ z273=0O Writing 9? =— 1, we obtain 
Ee” ent t 
Wi Zi 
ee re IgA Fe 09) (12209) (9) 
1 0" l 
= Den == DT 
80° (1—o)? 160 
Denoting by >, the sum of the pt" powers of the roots, and 
observing that e*—1, we know 
D2) == Oh =S (, == 2, 0} 
and generally, & being an integer number 
Zar, Zug), Zire, Zuppa 0. 
Therefore 
W, i 160 Dan 1 
which gives different values for different values of 7. 
According to 
n=4p, 4p+1, 4p4+2, 4p+3 
we get respectively the four values 
Wa fo, i, 6 1) 
STE ’ ? ’ 
For W, the equation (6) gives 
1—a2'=0 
or 
lte+e7+a*4+ aet*—0 
thus 
w dz >S oe” ent t 
TT Se ee SS OEE) 
Putting 
nt—lg (1—ge—')—lg (1—97e —2')—Iq (L—e—5 tlg (1—e— 10 *) lq (1—e— 204) 
Ke —e 
6 
and reducing by means of the equations (a) and (6) 
20? 35 40? 525 
D= e = t 4 5 + - e 
x ete lo 1—o’ 2 2(1—e)? 2(1— 0’)? 24 
E 1000 (1—e) (1—0?) # 
we get 
= 9 60? 
WRS 5 n° + gele n+ 
200: (1—@) (1— 0”) re 
= rn 525 340 + 9807 — 420° — ae] 
2 Gens 
