270 
a 
Zr 
$< 
55) 
PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 
HS 
Case (2), {=8#2. For definiteness assume E<£ and let 
{=2e. Then £>0 and there exists T<oc such that 
2,=<C+e=%-¢ forall £&T 
If now in (43 a) we take o=o0, z}=2, x'=#=g(8) for all #>o. 
then, 
T+ 
(56) Up = fa) — û) dt < u 
rors 
[, a 
J (9(z0—2) dt + 2p — 24x | =- 
_T 
—o (T* MT +8 
where by (38), (40), 
=u Nz —gz—2) > o 
© 
> 
A _ 
— UU + 2 
Hence Ur, = Ur + Urs diverges to - oo as T*—oo in this case, 
and by similar reasoning in the case £<¢, hence in the entire 
Case (2). 
Case (3), {=C=2. In this case clearly 
37 
. A 
lim z, = 2 
Teo 
[t follows from the third member of (54) that 
G-EU- +4 ° ZT 
4] Koopmans - pag. 46