Full text: [Allgemeine Analysis] Theoria combinationis observationum erroribus minimis obnoxiae (3. Band)

474 
NACHLASS. 
[7-] 
JB(aM) 7 .P(a?V) = Product aus ^ 
. P(a?, \).P[oo,y) 
. {P (a?, s) .P{po,y) — S(a?, e) . Q(a?,y) j 
• jP(a?,££).P(a?,^) — S(a?,££). Q(a?,y)j 
. {22(0?, £ 3 ) .P{x,y) — S(a?, £ 3 ). Q (a?, y) j 
. jP(a?,£ 4 ).P(a?,y) —S(a?',£ 4 ). Q(a?,y)j 
. j P(a?, s 5 ) .P[oc,y) — S[oo, £ 5 ). Q (a?,^) j 
. jP(a?,£°).P(a?,y) — £(a?,£ G ).Q(a?,^)j 
= K(* 7 .1 ).P[x,yf- +7 ^.P[ X ,y).Q[ X ,yf 
worin £ 7 = 1. Zum Beweise dient, was sich leicht nachweisen lässt: 
*P[oo, zy).P[oc, ~) = P{xx,yy).P(ocx,z^)-\-R[xoe,yy).R[xa},z^) 
-P(g,y)*+ Q[x,yf 
2 P[xx, l) 
P ( ^ ) + E^LM , R[m 
= P{*,yf 
R ( x ’ £ ) 2 nr r f A* £ ) a 
-R(a:, l) 2 ^\ x *y) ' JR{x, 1)* 
[8.] 
P(a?, 1) = p , 
Q(a?, 1) = q , 
P(a?,l) = r , 
\}> =■ oo— 2a?a?-f-4a? 3 — 4 o? 4 —j— 6a? 5 — 8 
\q = — oo — 2a?a? — 4a? 3 — 4a? 4 — 6a? 5 — 8, 
xdp / 
pdx P 
¿cd r / 
rdx ~~ r 
? 6 + 8 <^ 7 — 8a?'-f- 13a? 9 — 12a? 10 .. 
? 6 — 8 a? 7 — 8 a? 8 — 13 a? 9 — 12 a? 10 .. 
4r = l-f-8a?a?—8a? 4 -f-32a? 6 —40a? 8 -f-48a? 10 —32a? t2 + 64 a :?1/i — 104a? 16 -{-104a? 18 . . 
Coefficient von 
00' 
fa*b 6 c v . 
wenn a, b, c .. 
Primzahlen, wird 
Ä 
a a+1 — 1 
a — l 
b 6+l —i ci ,+i — i 
b—1 ’ c — l 
[worin für jene drei Reihen folgeweise] A — 2**(—1)^ +1 , A = 2 ft > A= 8(3—2^)
	        
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