Full text: [Nachträge zur reinen Mathematik] (10. Bandes 1. Abteilung)

346 
ANALYSIS. NACHLASS, 
[*) In der Handschrift steht hier »und«.] 
Aus der Verbindung der Gleichungen (15) und (19) folgt 
ß(a — Y)a?F(a,ß-h 1,T+1) 
— T (T — 1) F{a, ß — 1»T — 1) H“ T (T — 1 +(ß — a)x)F{a, ß, y) = 0. 
Also für unsern Fall, wo a — 4, ß = "{~ii 
— (T ~ Y?%F{h T + F, T + *) — T(T “ !) F ih T — h T “ 1 ) 
+ T(T “ 1 + (T - 1)^) F ih T“ M) = °- 
Es ist folglich, weil 
AW 
proportional sind 
T (T — 1 ) F ii > T— i» T — 1 )»(T — I) T T — y, t)j (T — I) (T - i) ^(1 > T + h T + 1 h 
allgemein [*)] 
(43) (T-|)^ ,i “ 2, -(T- 1) (/+7)^- ,) +(T-i)^ <T, = 0, 
also 
A< W) - 2 (/+ y) A + 3 A" = 0, 
3 A — 4 (/+ yj A" 4- 5 A" = 0, 
5 A" — 6 (/+ yj A'" -(- 7 A IY = 0 etc. 
Man setze 
('44'j 2 1 + ff A> — B<> 4 1+/’/’ A" _ 6 1+// Ä'" t 
1 f A 0 n 9 3 f A' n ’ 5 f A" n eiC ’’ 
so wird 
f45) B° 
-K 
9/ f 
1 "'l +ff ] B ' 
, ^' = 
25 / f 
24 
-, = 
/ f ! 49/ /-y 
U + /77 48 U +/77 
B' 
etc. 
[S. 43] 
Nun ist aber auch
	        
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