ZUR THEORIE DER TRANSSCENDENTEN FUNCTIONEN. I. 
301 
t = P( 1 -x s -x' 7 + x™ + x 6i ) + Q(l-^ 7 -^ 3 + ---) 
u = P (1 - x 7 — x' 3 4- .T 34 + x™ )-\-Qxx{\ -x 3 — x n -+- x 26 + Æ 54 . • •)• 
Man findet aber auch durch ein ganz ähnliches Verfahren 
(1 — x 3 y)(\ -f-x k y)(\ + 
a?_ 
y 
-p^t-otor-j+ Q ** 
y-*'V + 
x , x 
y ' y 3 
Hieraus folgt 
tx + w = (P+ Qx)\l+x-x i -x'-æ l3 -æ l8 + æ 2, + « M -..) 
-tx + u = (P-Qx) jl -x + x'-x 7 -x u + x K -x” +x u ...\ 
oder 
tx+u = (P + Qx) [- X 5 ] (1 + x) (1 - x‘) (1 - x°) (1 + x”)... 
u - tx = (P - Qx) [- æ 5 ] (1 -x) (1 + X s ) (1 + X 6 ) (1 - x?)... 
Nun ist ferner 
[P + Qæ)(l -x-x w + x n +---) = -^-(1 — xx+i?— x?-x H +x a -\-x u ...) 
= - vl-* ä ](> -xx)(\ -M 5 )(l + x 7 )(l -x s )... 
(.P-Qx){l-x-x K + x u +■■■) = + xx-x‘-x?-x' , -x , ' + x' > ■■) 
= —(I —x s )(l -æ’)(l + x s )..., 
P+Qx = (1 - xx) (1 + æ 5 ) (1 + *’) (1 - ®*) • • • 
P — Qx = (1 + xx) (1 - x 3 ) (1 - x 7 ) (1 + x s ) ■ ■ ■ 
tx-\-u = (1 +Æ S )“(1 H-æ 15 )'-" 
.(l+»)(l-ii®)(l+ai*)(l-äS*){l—-**)(! +x'‘)---