133 
. | a6 . 
CIRCA SERIEM INFINITAM 1+ r; y ^+ ETC - 
itum sit 
er art. 7 
VI. 
0 = yF—y(l—00) F"—(y — ol—6 — i)xF"' 
tertiam, 
Hinc atque ex III, eliminando F" 
»erspici- 
ictiones 
VII. 
0 = y F— (y — cl—1 — t)x)F" — (ot-J-1) (l—x) F 
functio- 
Porro ex IV atque V, eliminando F"'" 
it aham 
mentum 
VIII. 
0 = {y +1) F" - (y+1) F""+ («+1 )xF 
xem ge- 
Hinc atque ex VII, eliminando F"", 
'ones ad 
IX. 
0 — y(y-f-l)F—(y —j— l) (y — (a-f-b-f-\)x)F"—(a+l)(^+l)®(l 
11. 
Si omnes relationes inter ternas functiones F(a, b, y), F(a-j-X, 6 + T ~l" v )» 
F(a-f-X', y-j-v'), in quibus X, |x, v, X', p, v' vel = 0 vel = +1 vel = — 1, 
exhaurire vellemus, formularum multitudo usque ad 325 ascenderet. Haud in- 
functio- utilis foret talis collectio, saltem simpliciorum ex his formulis : hoc vero loco suf 
ficiat , paucas tantummodo apposuisse, quas vel ex formulis art. 7 , vel si magis 
placet, simili modo ut duae priores ex illis in art. 8 erutae sunt, quivis nullo 
negotio sibi demonstrare poterit. 
[16] F(a,g, 7 ) — F(a,6,7 — 1) = — ®+ 1 >7+ 1 ) 
[17] F(a,-6+l, 1 )-F{a,-6,y)=jF[a+Ut+l.y+l) 
[18] F(a+l,g, T )-F(a,6, r )= yF(a+1.6+l,7+l) 
[19] F(a,6 + l, 7 + l)-F(a,g, 7 ) = y^F{a+l,g+l, 7 +2) 
rt7 ) ; [20] F{a+l,g, 7 +l)-F(a,g. 7 ) = ^i=^F(a+l,g+l, 7 +2) 
[21] F(a-l,g+l, 7 )-F(a,g, 7 ) = ( i=y^-F(a,g+l, 7 +l) 
[22] ^(a+l.g —i, 7 )_F(a,g, 7 ) = i^^yX ) -F(ct+l,g, 7 +l) 
[23] F(a-l,g+l, 7 )-F(a+l,g-l, 7 ) = fe^F(a+l,g+l-7+ 1 )