Log-Arcsine Algorithm

[Albert Chan]

Here is a table of initial conditions, for all inverse trigonometric / hyperbolic / log functions

s(n+1) = s(n) * √(2*s(n) / (s(n) + s(n-1)))      → s(∞) = func(x)

Code:

asin    x*√(1-x²)       x
asinh   x*√(1+x²)       x

acos    x*√(1-x²)       √(1-x²)
acosh   x*√(x²-1)       √(x²-1)

atan    x/(1+x²)        x/√(1+x²)
atanh   x/(1-x²)        x/√(1-x²)

log     (x-1/x)/2       (x-1)/√(x)
log1p   x*(1+x/2)/(1+x) x/√(1+x)