Hi, I was recently viewing a Wikipedia article on Lambert W Function. I was going through the identities and found this identity:

W1

.PNG

Download PNG • 2KB

It says that it is true of all x>= than -1/e. I typed this identity in WolframAlpha and inserted a value of -2/e, which is outside the given domain. And here is what I got

W2

.PNG

Download PNG • 33KB

It says that it is true? How?!!

Also, another identity:

W4

.PNG

Download PNG • 3KB

According to my observation, the given domain should be 0<=a<=e

W5

.PNG

Download PNG • 20KB

W3

.PNG

Download PNG • 20KB

I forgot to mention that ln(2) -1 + pi(i) is the principal value

Thanks for the explanation. So, it means that input value can be any real number. 😊

@Omair Siddique You're quite welcome. As long as you allow the output to be Complex.