HP49-50G Lambert function

[Gil]

Thanks for the detailed explanation.

For negative numbers, I get the same complex numbers as when using Wolfram Alpha, and that up to -190.
Beyond that number, I get different — but possible, correct — results.

My program
W(-190.,0.): (3.73813626409,-2.54403205829)
= result given by Wolfram.

But
W(-191.,0.): (3.0807478,-8.212851).
not equal W(-191_Wolfram Œ): (3.742525,2.544493).

Strange?

Could you have a check in your program for w(-191 + 0i)?

Thanks and regards.

By the way, when solving for
x^2 = 2 ^x,
I find only 2 real solutions : -. 766 and 2; no way to find by calculus the missing real solution x=4.

Could you help me?

Regards,
Gil Campart