Lambert W Function (hp-42s)

[Albert Chan]

(09-28-2020 04:06 PM)lyuka Wrote:  y0 = 1 / e + sqrt ((2 / e) * (x + 1 / e)) + 0.3 * (x + 1 / e);

Thanks to sqrt in this equation, in 42S we can automatically get the complex y0 from x less than -1 / e.

Very nice approximation !

However, the formula might be too good. At x = -1/e, above return *exactly* y0 = 1/e.

With f(y) = y*ln(y) - x, f'(y) = ln(y) + 1, we get f'(y0) = -1 + 1 = 0

Unless we test for zero slope, Newton's formula, y -= f(y)/f'(y), will crash with divide-by-zero.
You might want to adjust the formula a tiny bit ...