Want to point out that there are far superior methods:
http://math.eretrandre.org/tetrationforu...70#pid7470
http://math.eretrandre.org/tetrationforu...12#pid7512
and below.
This code calculates arbitrary branches of the Lambert W function for arbitrary inputs and is extremely fast (I can get thousands of digits of precision in a fraction of a second on my machine) by using Newton's method.
http://math.eretrandre.org/tetrationforu...70#pid7470
http://math.eretrandre.org/tetrationforu...12#pid7512
and below.
This code calculates arbitrary branches of the Lambert W function for arbitrary inputs and is extremely fast (I can get thousands of digits of precision in a fraction of a second on my machine) by using Newton's method.

