210 
NACHLASS. 
quibus valoribus in 80 substitutis, fit dividendo per x^ 1 
0 — P' \afix— (y—[a-\-fi-\-\)x) [X — (1—<z?)([A{jl—p)j 
■~^rÎT“ (a+ô+l)<i?+2|x(l — x)]x 
1 
Multiplicator ipsius P' in hac formula fit divisibilis per x statuendo p = 0 vel 
p = 1 — y; valor posterior producit 
0 = P'{afi-f-a-f-^-j-1 — 2y— ay—^T+TT) 
Comparando hanc aequationem cum 8 0, cuius forma prorsus similis est, patet 
quae illic fuerant P, a, fi, y hic esse P’, a-J-1—y, fi-\-i — y, 2 — y: quare 
quum illius integrale completum assignaverimus, manifestum est, P' contentam 
fore sub formula 
P' = MF[a-J-1— y, fi-\-\—y, 2 — y, x) 
-\-NF{a-f-1'—y, fi~\-\—y, a-J-^-J-l— y, 1 — #) 
denotantibus M, N quantitates constantes, sive 
[83] Fia, fi, y, x) ■=■ Mx l ~^F{a-J-1— y, fi-{-l—y, 2 — y, x) 
-{-Nx 1 ^F{a-\-l — y, fi-\-l— y, a-\-fi-\-\ — y, 1—x) 
ubi constantes M, N ab elementis a, fi, y pendebunt. 
42. 
Ex aequatione 82 sequitur 
F{a-f-1—y, fi-\-l — y, 2—y, x) = (l — xy a 6 P(l — a, 1 — fi, 2 — y, x) 
F[a-J-1 — y, ö-J-l—y, a-J-6-J-l— y, 1—x) — x^Fia, fi, a-\-fi-\-\ — y, 1 — x) 
unde statuendo 
N 
= f{a, fi, y), 
M 
N 
= c/{a, fi, y)