The Solution of $S \exp(S) = A$ is Not Always the Lambert $W$ Function of $A$. Corless, R. M., Ding, H., Higham, N. J., & Jeffrey, D. J. In ISSAC '\textup07: Proceedings of the \textup2007 International Symposium on Symbolic and Algebraic Computation, pages 116-121, New York, 2007. ACM Press.
doi  bibtex   
@inproceedings{cdhj07,
  address =       {New York},
  author =        {Robert M. Corless and Hui Ding and Nicholas J. Higham and
                   David J. Jeffrey},
  booktitle =     {{ISSAC} '\textup{07}: Proceedings of the
                   \textup{2007} International Symposium on Symbolic and
                   Algebraic Computation},
  pages =         {116-121},
  publisher =     {ACM Press},
  title =         {The Solution of {$S \exp(S) = A$} is Not Always the
                   {Lambert} {$W$} Function of {$A$}},
  year =          {2007},
  doi =           {10.1145/1277548.1277565},
  isbn =          {978-1-59593-743-8},
}

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