ZUR THEORIE DER TRANSSCENDENTEN FUNCTIONEN. I. 
295 
[6.] 
[S. 4 4] 
Durch Induction haben wir gefunden: 
1 4- X X 5 + X* 4“ 07 16 4-0? 21 + X 33 - • . 
= (1 4- OC) (1 4“ OL- 5 ) (1 — JT 6 ) (1 4- X 7 ) (1 4- Æ.’ 11 ) (1 — X n ) (1 4- Æ 13 ) (1 + OC 17 ) (1 — <0 (1 + ■V 19 ) 
\xxY\pc?] [a; 12 ] [æ G ] 2 [ — x\ 
~~ "M[/][i 6 ] ~ [~x 3 ][xxY 
= (1 —x 3 — x J 4- # 18 4- «a? 80 •. •) (i 4- x){ 14- oc 3 ) (1 -\-x 5 ).. 
(y Ä 4* ^r) x ''+(y u +y) x ™ etc ‘) i~ü x ^yy x ‘ ~ï~ y <r ' ß x ' & * * ’) 
y x + Yÿ xk +y K x "' + Y X%Ò ^ 
( 1 +(/+4 x--+(/+4 jc'-■'+■ ■ ■) 4LV ’ 
Factor 
Also 
[æ 18 ] 2 (1 -æ ,s ) (1 -a:’ 8 ) (1 -æ 36 ) (1 -x 3a )... 
44®] ~ (1—x e : (1 —a? 12 ] (1 —œ 21 j (1 —£C 30 )... ' 
(1 — 2 O? 36 4- 2 T 1 
■\{x — x iô — x il) 4“ ^' 21 4* etc.) 2 4- [x'' 
^ ,f! Y'* 
4~ x m) 4- x v ™ — etc.) 2 1 
= (l-2^ 2 + 2* i8 -2*'" )8 + etc.)^^. 
I*T Irjwi „6 [*' , №T I _ [*T[*T 
[x 72 ] I 1 J “T“ x [x aG f [a; 24 ] 2 i ~ [x**][x 6 ] * 
Also 
[x\[x*f[x G Y 
[x][x"Y _ . 
'* r^aiar«.«! 1 ’ 
[xxY[x 9 f[x tz ï ' [a: 8 ] 3 [x*] 
[a? 2 ]’ 4 = 16 x\xf |> 4 ] 16 4- O] 16 [V] 8 . 
[7-] 
Durch Induction ferner gefunden: 
1 4- x 4- x 2 4- x * + oc 1 + X ' Z + oc 15 H 
= ( 14- x)(i + X 2 ) ( 1 - x 3 ) (1 4-07 4 )(i 4-<2? 5 )(i — # c ) ( 14- oc 1 )( 14- * 8 ) {1 - x °) • • • 
(1 —a; 3 )(1 —as®)(1 —£C®)(1—¿e**)(1 —¿e’ 5 )(1 —a:' 8 )... _ [xx\{x 3 f 
— (!-*)(! —x 5 j (1 -x 7 ) (1 ■-»“) (I —Æ l3 J (1 - æ tT ). .. [a:] [a: 8 ]