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

100 
W. ScHEIBNER, 
44 
x — x„ = 
k m: - </« 1 - y)'+i l ti/'o 1 - / + io»?] 
2 [L\ - Ä/> 0 ) I — </)' 4- ,M [(2 /, - L, I - i/-; 4- | ll :i+y+ //' I 
2 (ft> - W 1 - // 2 - ."/o I - r 
2 (*/o - £„') (l-y)*+ li/o ( 1 “ y*) - Io >?] 
00 - V. 1 - // 
/o- 
u i 4- // 
Io*? . _ i r , tirzMi l ~U 
l — y 1 4 ' 0 2 ¡.l 14-// 
i - ,y = /< 
W ixx () 4- « — 2/. j; — ,x' 0 
c c 
?o s 
2 U r , ’cCiT 0 ) 4- /< — 2Ä] VF J'J'u 4- 2/i |/i — *} (£C — J2 0 
2 Ll (X — ' ,ii 
VF (ar£C 0 ) 4- (fl — 2 *) [x — ¿C 0 ) 2 4- | 0 £ X — 4- -.4 /t 
Der letzte Ausdruck liefert sogleich 
IV" (xx 0 ) — 2 l (x — £C 0 2 4- £ 0 £ 2 Y — *) 
VF ¡5C£C 0 ) 4- //. — 2 Aj (iE — x 0 ) 2 4- | 0 £ V — A4- | ll 
folglich 
« *-±1 = + _ 2 l = 2 ,V _ A: 
' 1 —y [x-xtf 
übereinstimmend mit dem vorigen Artikel. 
Die Werthe der Radicale £ und // endlich nehmen die Form an 
£ = 2 /i {I — y) X 
Mi 1 ~y) + 'lo/o.y (I +y)— 2 Io (y 0 - V.) ( :1 — y) [3 Ä (I - r) •+• ,M I + y + y~ 
r] = 4 t u üc — j' 0 
(I ^/o - 0o') ( 1 - y) 2 + i« ti/'o' ( 1 - y*) - Io f /]) 2 
l/, 0 a?a? 0 4- it/ 0 (a? 4- a? 0 ) 4- ,V 0 ] £ 4- [hxa\ 4- Jl/ c 4- a 0 - 
2 itf o a? 4- xV 0 4- ¿1— 2* ./■ - x 0 - 4- £ 0 £) 
VJ|„ 
(L 0 x- 
23. 
Wir wenden uns zum dritten Beispiel für die Anwendung der 
allgemeinen’Formeln und untersuchen den Specialfall 
'<!( = S = o oder a., 4 = ««, , c, 2 = cc* 
Damit folgt 
<; = 3 gts_433® , n = ($(2$$-£6) ;i
	        
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