406 
NACHLASS. 
cos lemn cp = i_cpcp-f lcp 4 -^cp 6 + ^cp 8 -^cp 10 + 
1200 
r 
”} = 1 +T'P'f-^ < f 4 +57;'i>“4 
40320 
403200 
<P 
10 
37 
.12 
113 
4151347200 
.14 
4171 
159667200 
.„16 
6974203296000 
Formulae pro P, Q, p, q in infinitum continuatae quavis convergentia data 
citius convergunt, formula autem pro sin lemncp diverget, si cp ponetur 
sive cp 4 y, formula autem pro cos lemn cp diverget, si cp «5 
Einige neue Formeln die Lemniscatischen Functionen betreffend. 
Essei = <P. oder tp = * + H**+^.y4 
1.3 1 ^<J , 1.3.5113 
uu 
2.4.613 
Man hat dann 
i 3 1 0 i 3.7 1 in, 3.7.11 1 1,4 
cp cp = xx-\— -—x-A . — x-4 . — x 1 . 
• * 1 R S * R Q R * S Q 1 Q rr 
5.9 5 ‘5.9.137 
Es sei x = sin lemn cp, y = sin lemn cp, z = sin lemn (cp -f- cp) 
so hat man 
„ aV(l—y*) + y\/(l — x l ) XX —yy 
\ + xxyy 
/1—zz _ — 2xy -t-y/(l — ic 4 )y/(l — y*) 
’'1 + 3Z l+®® + yy—xxyy 
J 1 ~ z * + —**).—_y(Hl. ai *)^( 1 — y 
* zz 
*V0 —y*)—yv^O —* 4 ) 
i — a;« — — x %yy 
2xy + \J{i—x ,l )\/{\—y l ) 
(l + xxyy) [xx — yy) 
JU g i\ __ (i—xxyy)\J{\ — a: 4 )y/(l — y*) — 2xy{xx + yy) 
* ' (l + £#2/J/)® 
. / / ^— ^C 1 —aaWQ—yy)—■*W(i + gg)v^0 + yy) 
* ^ ' l-\-xxyy 
1 / (1 _1_ zz \ — >/ i + xx)^{l + yy) + xy y/(l— xx)\J[\—yy) 
' ' 1 -f- xx yy