Compute the infinite product
[sin(x) cos(x/2)]^1/2 · [sin(x/2) cos(x/4)]^1/4 · [sin(x/4) cos(x/8)]^1/8 · ... ,
where 0 ≤ x ≤ 2π
list
10 for Xn=1 to 20:X=Xn/10
20 Deno=1:Deno2=2:A=1
30 for F=1 to 60
40 Fctr=(sin(X/Deno)*cos(X/(Deno2)))^(1/(Deno2))
50 A=A*Fctr
70 Deno=Deno2:Deno2=Deno2*2
80 next
90 print X,using(1,8),A,asin(A)
100 next
run
x expression arcsin(expression)
0.1 0.04991671 0.04993746
0.2 0.09933467 0.09949876
0.3 0.14776010 0.14830313
0.4 0.19470917 0.19596094
0.5 0.23971277 0.24206998
0.6 0.28232124 0.28621292
0.7 0.32210884 0.32795621
0.8 0.35867805 0.36685132
0.9 0.39166345 0.40243879
1.0 0.42073549 0.43425591
1.1 0.44560368 0.46184848
1.2 0.46601954 0.48478658
1.3 0.48177909 0.50268383
1.4 0.49272486 0.51521835
1.5 0.49874749 0.52215311
1.6 0.49978680 0.52335261
1.7 0.49583241 0.51879310
1.8 0.48692382 0.50856438
1.9 0.47315004 0.49286296
2.0 0.45464871 0.47197777
OK
Edited on December 29, 2013, 1:28 pm
|
|
Posted by Charlie
on 2013-12-29 13:26:28 |
computer exploration--table of values
