Full text: Theorie der analytischen Functionen

346 
Sechstes Capitel. 
Im ersten Falle ist 
-M ^ (a v — b\* 
V c -* = V -* ( av ~ l Y 1 = 
¿éi( x - a vY K ~by-\x-b) ^^* 
_ V C ~* I JC I *(*+1) /X- 
(<* v — ft")* \x — b) | ' 1 \a: — h) ‘ 1.2 \ x — 
, *(*+l)(* + 2) ( a v- h V , \ 
+ 1.2.3 \a:-&y ' * " j 
und die Coefficienten A ( Y werden der Reihe nach 
AM = 0 
AM = 
a„, — & 
AM = 
AM = 
M 
C M 
— 2 
— b 1 (a v — by 
J.r) 
L - i 
O cM 
2 c —2 
,(v) 
- 3 
:,-6+ 1! (o,-i))2 + (a v ~bf 
a¡:' = 
c —\ . ,a — 1 c —2 , (fi— l)(fi— 2) c —3 
— X | ,<* x ¿ | 
— & ' 1 ! (a v - &) 2 ' 
2! («„ — &) 
3 H 1" 
,(*0 
, (fi — l)(fj— 2)... (fi— (r — 1)) C_ r , _ , 
' lv — i^' (a„ — &)»• ' ' (u. 
(r — 1) ! 
usw. Im zweiten Falle hingegen wird 
(v) 
—fi 
( a v by i 
y c -» „ V(_iv44 l_ 
2 !( l) x c ( I? x j y f x\ , x()t+l) / a; \ 2 , «(*+1) («4-2) ( %V , 
V 1 +iy+-T^Uj + —ü%r»~ \a,) + ■■■ 
und nun gibt der Vergleich der Coefficienten 
r» 
X = 1 # = 1 a v 
x z= 1 a v 
. . . AM = 'S 1 ( li* x (* + 1 ) •••(” + ft ~ c 
V ¿-JA ’ 1.2...ft « 
¿’(-O* 
(*) 
(ft + !) (ft + 2) ... (fi + v. — 1) c —x 
1.2 (x — 1) 
x >
	        
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