496 
but also by means of other series of which the terms diminish 
more quickly; for, if g represents an arbitrary integer positive number, 
Lee gt! Segre 
Snipe == = C (20) = 
pet ae @ s (20) 
y b | p=1 2 
2 ed y 2¢ ge 9 o 4 y 26 
Er bs [seo — ER 
Yael 6 mi Ural bx 
2 @ fy \?F ga de! ek! 
== 2 le 6 Gp). Er RCA 
Yel, 0 Ll arr x r=) 6%—-y I 6%-+-y 
and therefore 
| 
d co y2e—1 q 1 
render [yn SE Js (20) — > ld + 
gl may “er 
ml 
1 1 
q (1— jn (l—y, 2n 
nb VO Bf SLES 
x1. Ox— y i 
0 0 
Now is 
= as i 
6%—-y Be * *. (6% —1) + (1--y) 
0 0 0 
1 1 
(1—y)2” *(6x—1)2" (6 ad een 
a dy = — di 
eas 
‘ ] 
= — (6x —)*" log (: — al + = (-—1l)r. ; —1)2"—? ; 
5 bx p=1 
sek 
1 
a (6x + 1) 2n (6x + 1)2»—(1— y) jn 
f- —— w=f 5 -dy — dj = 
6xty ° Gety - (6x+1)—(l1—y) 
0 0 0 
1 = 
= (6 + 1) ng (1 Dj: > (6x + Ie; 
Oz = Sp ¢ 
so the calculation of / (27,2) is to be reduced to the calculation of 
the integral 
fi yy?" Zen 
ee 
&(20) — = 
ue tne ¢ a 
{(20)— = == dy==2,(2n)! = — 
x24 gl (20)(20 + tp (20 be AE 
nie the ratio of two consecutive terms of this series is smaller than 
1 ; 
ze, so that, if there is a breaking off in an arbitrary place, 
6° (g+ 1)? 
the rest-term is smaller than the term last used divided by 
6? (¢ + 1)? —4. 
