LEMNISCATISCHE FUNCTIONEN II.
421
[13.]
Rechnungen zur Lemniscata gehörig.
|(sin lemn-|-{D) 2 -(-(sin lemn-^cö) 2 | 3 = 14y/5 — 30
j (sin lemn fffi) 2 — (sin lemn-f-tö) 2 j 2 = 10\/5 — 22
4 (sin lemn f co) 4 —}— \ (sin lemn -f ffi) 4 = 6 y' 5 — 13
= 0.4164078649 9873817845 5042012387
j 4(sin lemnf öj) 4 — i(sin lemnf®) 4 ) 4 = 340 — 152 y/ 5
= 0.1176674200
3196614580
5602352846
daraus Radix
0.3430268593
0761971797
7310507555
also
(sin lemn fco) 4
= 0.0733810146
9111846047
7731504831
(sin lemn-f-iö) 4
= 0.7594347153
0635789643
2352519943
(sin lenin-f®) 2
= 0.2708893033
8999814497
30710
(sin lemnfffi) 2
= 0.8714555153
9155336074
646029
QtV®
= Vii cos^Vtc + I-
sin T V7c)
QtV®
= v^(i cos t Vtc — i
sin T VTt)
[14.]
Lemniscatische Function.
/•da: r dJ ^
J — ? ’ J S/(1-X*) ““
Es verhalte sich 1
oc
\J[ 1 X OB)
\J (\-\-xx)
wie p
9
r
s
und 1
X
S/0-XX)
V(1 + X3
wie P
Q
E
8
so verhalten sich die cp -j- 0
entsprechenden Grössen
65741
01228
85731
80010
51472