Full text: Zur Reduction elliptischer Integrale in reeller Form ([Hauptwerk])

98 
J W. $CHEIBNER, 
f = % 4 — 6Ay s + (£ 
g = 21Ay 4 -+- [6 i~ — 0 y -+-Ci/. 
^ =/ry^f-dj 
k — %y x — 6 ly' 1 -h (S) g — If) — \-ify~ 
j~ = 4,y [%y-~ 3 A) g - lf - 2 u-fy 
[42 
f \'/ 
= ( a 2 (5% 4 -(g) 
¿y 
i = 20 n'fLy* 
= 9ty 2 -A 
= - 2 ly , 
M = ®-iy- 
«* = »V + i'-jG , 93?, = 2^-i-G) , 91, = (SÄ + (r-|i;)/ 
# 
Setzt man hier y 0 = i , ; /0 = o, so ergibt sich Art. 9 zufolge 
£ — 2 pY 0 (y - 1) + [2 (fl - 3 A) ,y 0 - A/o - »r/oj // - 1 )* 
— ,« Yoiy — i) i x ~ J 'o) *+■ /*'.(91 — <§• ./• — üT’o ' 
+ 1.(91 - 3 A) {9' - A/o) - Y. u VoJ [y - *)’(* - J Y 
- ^ M 2 [/„" — 2 (591 - <5)](y - I )[x - x 0 )- 
-+- \ [ 9t - 3 A) JjH A/ n "; - y7' 2 (/o"- 891)](y - 1. 4 (a; - .r 0 , 2 
Substituirt man hier die Wurzelvverthe 
21 = 3 A — /t , (£ = 3 A ■+■ ju , wo (.1 = V12 A ? — G 
so folgt wegen 
8.y.+s». = «- 3 a = 3 A-e= ^(9i-e) = --(«-«;■ = -/* 
4 = 2/ r 0 (i - y) -jf # +2 ’) (1 - y) V /; (I - y) >' - a? 0 ) - 2 ,u (a> - <r 0 ) 5 
- (7/0 + ) (1 ~ yri x - *•) + (y/o - 4 A + 2 (1 - y) (a? - ,r 0 ) ä 
2 
— u 
3 * 
[rj:- 2i-+ f n+- »jv 
x n 
Für die nämliche Function erhält man nach den Formeln des 
Art. 11 mittelst
	        
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