Lambert W Function (hp-42s)

[Albert Chan]

(10-03-2020 04:31 PM)Albert Chan Wrote:  Let z = x+r, we have √(2/e*z) = -1.3*z           → z = 0 → x = -r

I tried to solve by hand. Can someone check if this is correct ?

√(2/e*z) = -1.3*z
√z * (√(2/e) + 1.3*√z) = 0

√z = 0, or -√(2/e)/1.3 ≈ -0.6598

Because of square root branch cut, Re(√z) ≥ 0, thus we are left with z = 0