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

XII 
W. ScHElBNEK, 
156 
i) w —-——sin 1 Ult 
1 i -q™ 
- rok + ^Tzk [I - (-?)” C0S2 ' 1 “] 
+ ll, W + I 6^^, ( I 
,n- 4 U( l 
i - q 
sin nu 
7 
►-i w 7” 
2 
l—(j 
Sill nu 
{&&g TT“) =1+8 'S 7 (— i) 11 ——— (cos 2?im — g’ 
\ 3 # 3 w/ —i_ f/ 2wV 7 
= ^ 4 +i6^ r (-i; 
,»_i >*7 . 2 
II —;— Sin HU 
Sin n [-kn — u 
= k/ + 
\n ^7 • 2 
I —— sin nu 
&"u 
d-u 
i-q 
Bildet inan endlich die Gleichungen 
ö ig&u 0 f nq' 2n [m — i) q ln ~ 1 (cos2ii — <f n ~ 1 ^ 
+ f/ ~~M~ ~ ^ 1 T^v* + “ 1-20*”-* CO ^TW'* - ’ 1 
_ g -CTil" +f/“ (l + ?'**) cos2HK _ „ -CT 
^ (i-<7 s ”) s ^ i - 9 5 ”1 i-, 
q ( i + 7 . s 1 
1 n — 2 2 —Sin №U > 
2n J 
k "m Ö lg -¿G M . ^-7 i 
— = - 47 -4— = - I + 8 V 
4 ¿i ö q t 
n n \ 2 
w g 2 2 w g" 11 (cos 2 u — g“ n 
i — g“ 2il i — iq ln cos2M -+- g 4 ” 
I -+- 2 COS 2WM 
i - g 
=-.-8^ 
;i -9 
i — 4 cos 2 n u) 
d-^u Ö lg i}^u 
S^ii ~ ~ 4<? dg ” “ 1 
, \ 2 
-- +8 ^(rhs) (,+ 
8^ 
n q 1 n 2 n q~ n (cos 2 u + q 1 n ) 
11 — g 2n i 
2 q in cos 2 u -+- g 4 " 
} 
2 — I COS 2nU) 
= - 1 + & 2 
u 
-') n l' n f n 4sin , n« l 
l —q' n • 
2«.— 1 
Mg*,t* yi (2»-i) r~ (cos2M + q n ~ ) \ 
47 dg ^li-g 2 ” i _j_ 2g 2n_ 1 cos2w -+- g 4n-2 i 
Q ^q™+(-q) n (i +q* n ) cos2nu 0 v (-g) n f ! + g 2M . , ) 
= 8 Js —-- = 8 Js MM n - 2 rzk^ sin nu } 
d — 7
	        
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