DETERMINATIO SERIEI NOSTRAE PER AEQUATIONEM DIFFERENTIALEM ETC. 
229 
sed hoc labore ne opus quidem est. Patet enim, statuendo x = 0, fieri debere 
M=F{2 a, 26, a + 6 + i,i) = A 
difierentiando vero illam aequationem prodit 
+ 26 + 1. ot + 6 + f. !±£) 
= 2a«Jii’(a+1.6+l,*.®) 
+i(a+f) (6+i) A\Z®-F(a+f. 6+f. f. ®)++iV^ ^a+i, 6+*, f, *) 
unde statuendo a; =: 0 prodit 
iV = ¡A^^-F^a+l, 26+1, a+6+f, i) 
2 ct6 b(a-p 6-p-|-) II(—a) 
a -p 6 + |- ' II a II 6 
n(a + 6 — -*-) H(— f) r> 
FI (a — l) II (6—l) 
57. 
E combinatione aequationum 106, 107 habemus itaque 
[108] 2 AF{a, 6, a;) 
= F(2a, 26, U + 8 + +, ^) + f(2a, 26, a + 6 + f, i±^) 
[109] 2B\Jx.F{a+±, 6+i, f, ®) 
= i+Ja, 28, a + 6 + i, '-=£)-F{2a, 26. a + 6 + i, CA?) 
Mutando in aequatione 109 a in a — 4-, 6 in 6 — 4-, facile videbis, inde prodire 
[110] f.x) 
= f(2a'-i, 26 — 1. a+6 —*, 1 +±?]-F(2a~i, 26 —1, a + i—*, i=£)