Terminology
The Lambert W-function is named after Johann Heinrich Lambert. The main branch W0 is denoted by Wp in the Digital Library of Mathematical Functions and the branch W−1 is denoted by Wm there.
The notation convention chosen here (with W0 and W−1) follows the canonical reference on the Lambert-W function by Corless, Gonnet, Hare, Jeffrey and Knuth.
Read more about this topic: Lambert W Function