(28/48/50) Lambert W Function

[Albert Chan]

(01-29-2024 06:46 PM)Gil Wrote:  And why, in code post 19, did you define Y=R+R*X, that seems never to be used again?

(R+R*X) is just another method to calculate   Y = e^W(A)
It is only for compare against Newton method Y = (Y+A)/LOGP1((Y-R-R2)/R)

I was trying to decide which way does the job better.

(12-30-2022 11:27 PM)Albert Chan Wrote:  When I try to understand lyuka's eW formula (previous post), I found a better one.

e^W(a) = y = (y+a) / (ln(y)+1)

Let r = 1/e
If a = -r + h (tiny h), we have y = r + z (tiny z)

e^W(a) = (r+z) = (h+z) / ln(1+e*z)

Let H = e*h (known), Z = e*z (unknown), we have:

(1+Z) = (H+Z) / ln(1+Z)

H = (1+Z) * ln(1+Z) - Z = Z^2/2 - Z^3/6 + Z^4/12 - Z^5/20 + ...
...

I am skipping details of how to estimate Z from H.
Once we have Z, e^W(a ≈ -1/e) problem is solved.

e^W(a) = y = r + z = r + Z/e = r + r*Z      // = R+R*X of HP71B code