( 1—x m ) (1 - x m - i ) (1 - x m --) 
(l X) (l—xx) (l—x s ) 
-f- etc. 
1 — [m, 1) -f- [m, 2) — [m, 3) -f- (m, 4) — etc. 
quam brevitatis caussa per f[x, m) denotabimus. Primo statim obvium est, quo- 
ties m sit numerus integer positivus, hanc seriem post terminum suum m-\-\ tum 
(qui fit — 4~ 1) abrumpi, adeoque in hoc casu summam fieri dehere functionem 
finitam integram ipsius x. Porro per art. 5. II. patet, generaliter pro valore quo 
cunque ipsius m haheri 
m—1 
1 = 1 
— (m, 1) = —(m—1,1) — x" 
-f- (m, 2) = + (m—1, 2) -f- x m ~' 2 [m — 1,1) 
— (m, 3) = — [m — 1,3) — x m 3 (m — 1,2) etc. 
adeoque 
jn—1 
1 — x m 2 )(m- 
,m—4 ) [m - 
f[x,m) = 1—x 
v -t 1 
Sed manifesto fit 
(1 
(1 — x m ~~*)[m —1,2) = (1 
(I — —1,3) ==’ (1 
unde deducimus aequationem 
■1,1)+ (1 —x m ~ 3 ){m 
-1.3) —I— etc. 
x"' ~) [m —1,1) = (1 
x m b (m 
m—\\ 
m—1 
) f{x, m — 2) 
1, per formulam modo inventam erit 
Quum pro m = 0 fiat f[x, m) 
f(x, 2) = 1 — x 
f{x, 4) = (1—a?)(l — x 3 ) 
f{x, 6) = (1—a?)(l — <r 3 )(l — x 5 ) 
f{x, 8) = (l — a?)(l — <2? 3 )(1 — ^ 5 )(1 — x 7 ) etc. 
sive generaliter pro valore quocunque pari ipsius m 
Contra 
sive generalit 
Ceterur 
sione 
terminus ultii 
Ad sco 
impar: sed p: 
negativus est 
amplius abrui 
vergentem ea 
ipsius summa 
Per for 
ita ut valor fr 
terminis finiti 
fix, m) in pn 
Cresceii