Lambert W function (for HP Prime)

[Albert Chan]

(08-25-2022 03:17 AM)Bill Triplett Wrote:  Mr. Chan's code calculates cW(1.0E2028) = 4661.19.

"Out of this world?" Nope. It is more like, "out of this universe."

I have no idea how far the simulated HP-42S can go.

As high as you wanted. You can do above even on HP-12C.

a = 10^2028
x = ln(a) = 2028 * ln(10) ≈ 4669.642569      // guess for W(a)

x = ln(a) - ln(x) ≈ 4669.642569 - 8.448837810 = 4661.193731
x = ln(a) - ln(x) ≈ 4669.642569 - 8.447026860 = 4661.195542
x = ln(a) - ln(x) ≈ 4669.642569 - 8.447027248 = 4661.195542 = W(a)

With huge argument, convergence is quadratic

x * e^x = a
ln(x) + x = ln(a)

f = x + ln(x) - ln(a)
f' = 1 + 1/x

Newton's method (huge x), x = x - f/f' ≈ x - f = ln(a) - ln(x)