DETERMINATIO SERIEI NOSTRAE PER AEQUATIONEM DIFFERENTIALEM ETC. 
213 
Sed quoties 1 (7 — k) sive k-\-1 — f est quantitas positiva, demonstravimus 
esse (formula 85) 
/(oc — k, b — k, y — k) 
II (a + 6 — y — n (Æ — y) 
n ( a Tf)n(6—y) 
Quare quum k, quidquid sit y, semper accipi possit tantus, ut A + l — y evadat 
quantitas positiva, erit generaliter 
/(oc, b, y) 
II (a+ 6 —y)n(— 7) 
n( a y) n (6 y) 
et proin 
/(a + l-f, Ö + 1 —T, 2 — t 
II(a + 6—y) H (y — 2) 
n(a—1)0(6—1) 
ita ut formula nostra fiat 
¡86] F{a, b, oc —j——1— 1 — y» 1 /) 
+ n n^n°-ô- tH 0 - *r**- F ( 1 - a - 1 - g ’ 2 -^’^ 
sive mutata 7 in oc + b + 1— 7 
[87] F[a, b, 7, 1—oc) 
= <• •) 
+ n(7 n(l-on + (6l. T )(1-^ ^(1 ■1-6.7+1-a-«.») 
Si magis placet, scribere licet 
in formula 86 
pro (1 — ¿p)T -a-6 .F(l—oc, 1 —b, 2—7,oc) i^(a + l—7, b-j-1 —7, 2 —7, a?) 
in formula 87 
pro (1 —<*?) 1_ir F(l —oc, 1 — b, 7 + I—oc —b, a?)... .F{y — oc, 7—b, 7+I — oc—fi,oc) 
44. 
Quoties itaque elemento quarto in aliqua serie sub forma nostra contenta 
valor tribuitur inter 0,5 et 1 , convergentiae lentiori per formulas praecedentes 
remedium affertur, quippe quae illam in duas alias series similes dispescunt