Tree T and Lambert W - Jeffrey, D. J. (2021 23rd International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2021)
The paper discusses the two cognate functions Tree T and Lambert W . The definition of the Lambert W function in the complex plane, specifically the branch structure, has been the subject of varying opinions from the time W was named. These opinions are reviewed. Until now, the cognate functions have been regarded as simple reflections of each other. Here I propose that the two functions be given independent branch structures, thus allowing users of computer algebra systems access to whichever structure is convenient for them.