046 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28
For these values. we have
528-2)
i
À > —
2t)
and I/2w can of course be very large when w is very small (1).
First Limitation of the Value of A
520. Providing w is not too small, À will remain at a relat-
ively low level. Indeed, it mav be noted in the first place that
() We have
=
on
an
>t
Hu
Thus A will differ from its limit value bv less than e, i.e. we will have
2 (1)
,
nt
æe if
17 >
rE
Thus, if for example w=1/100, A will differ from its limit value 50 by
less than 1/10 for n > 3000. It can thus be seen that A can only have
very high values if n is very large, and such values are incompatible with
observed reality, at least as far as can be judged
11] Allais - pag. 250