Full text: Zur Reduction elliptischer Integrale in reeller Form (Supplement)

W. Scheibneu. 
„ ,*)■ ii />■ 1/, _ ¿b(on. n 1 
d'^ud'^u (21/, <y 2 ) sin 2 u 
— sin (4?i — 2) u 
8 sin 211 
Sill 2 U 
2(2M, q‘ 
1 — 2<7 4n cos4?< 4- </ 8 ” 
n in ~* 
= 8V^- sin (4 w — 2) ?/ 
d-ud-^u &{2U, q*) ^ - ~ 4W ~ 2 
= 8 sin 2U y 
+9 4»-*) 
I — 2</ 4 ” 2 COS 4 W 4- 4 
i d-uü u 2^92(7/, ?'</*) sj[— i) W 4 g n • 
3 6 ■e-AUiiqt) I + (-q) n 
= cot?/ 4- 4sin 2 uJ^J 
a 2 öjU&iU _ 2 (tl, »g* 
d-ud' i u 3 -5- 4 (?/, /V/-') 
= tgW 4- 4 sin 2 7/. y 
I — 2 (— </)COS 2 7/ 4* q 2 
Sin 2 nu 
I 4- 2 ( — q) n COS 2 77 4- r/' 
- I)V M 
w,M II „ . 2 VTr 
ttü-.. A = — 14-8 Sin 7/ > 
•'^, 77. tgM l ^ x _ 
— CO 17/ — 4 y 
1 f ty 
n . / T \ n jn 
'> < f > ; , -ÖT*- = Igw 14-8 cos 2 ?/- 
v'i» 1 1 
2 q* n cos 211 4- q* n * 
0'" . 2Ä' 
— Sin 2 7/7/ = — COtr/) 
2 q ln COS2 7/ 4- </ 4 " ^ 
71 q —sin 2 717/ = — X tgr/) 
I 4- r/ 2 ” ”■ 7 
I f . • 2 ^7 </” (i 4- 7 2n ) ) 
— < I 4- 4 Sin U > 3 i 1 
11U ^ 1 — 2f/ 2,i COS 2 7/ 4- f/ 4 ” ^ 
Sill 2 71 — 17/ = 
und wie sich durch Vertauschung von q mit —q und von u mit 
u -+- | Ti leicht ergibt:
	        
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