(28/48/50) Complete Elliptic Integrals

[Albert Chan]

(03-04-2024 06:11 PM)John Keith Wrote:  For m = .25, I get agm2(1, sqrt(.75) ~ 0.866025403784) which returns
b = 0.93180839162
s = 0.991019606076

Lua code had been updated, instead of starting s = a², it start at 0 (see post #7)
The reason is to produce as accurate E(m) - K(m) as possible.

lua> m = 0.25
lua> x, y = E.agm(1, sqrt(1-m))
lua> x, y
0.9318083916224482      -0.008980393923673079
lua> k = pi/(2*x)
lua> k, k*(y-m)/2 -- = K(m), E(m)-K(m)
1.685750354812596      -0.21828814547316888