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=£)