( 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