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

298 
ANALYSIS. NACHLASS. 
(1 -\-2x-\-2x i + 2x 9 -\ ) +(1 2x^ 2x 29 -] ) 
= 2(1 +rr)(l +£ 9 )(1 +iC 11 )(l -{-X 19 ) (1 +£ 21 ). 
. (i 4-P) (i - X u ) (i 4-* 16 ) (1 + * 24 ) (1 - * 10 j (1 -* 20 ) • • • *) 
= x* (1 -J-a)(l — X s ){\ — P) (1 4-V)(l 
. (i 4- xx) (i 4- x 4 ) (i 4- x *) i 1 + x *) i 1 — xW ) 0 + ^ i2 ) • • • 
[S. 4 6] 
[ll.J 
Zum Beweise der letztem Gleichung scheint folgendes brauchbar: 
(l+zy)(l-afy)(l — y)(l +y)(1 +*"y)( 1 -*'■»(* -4)(* _ 4)" 
wird entwickelt in 
1 -Vyy + x 2 V-® 7 V + 
— x u t/ s 4“ % iS y° 
x'° , X 62 . x' os , 
W “"T* - y 6 
4* Q i y 
y . « 
‘ y a 
4- 
wo P und Q blosse Functionen von x. 
vSetzt man y — x % , so verschwindet der in Q multiplicirte Theil, und 
man hat 
t _ ¿t; 8 )(i — p 2 )(i — # 88 )(1 — a; 32 )-. - = P( 1 — 2a? ,0 4- 2a? 4W — 2# 90 etc.). 
Also 
Setzt man hingegen 
so verschwindet das erste Product, und man hat 
P 8 ) fl —X s2 )... 
*) besser: 1+x 1-f x 3 1 +x* 1 +x 6 1-j-# 7 l-\-x d 1 — o; 10 l + # u 1 + x 13 1 + P 4 etc. 
1— X 3 1 — x 7 i — x 13
	        
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