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On the LambertW function

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Abstract

The LambertW function is defined to be the multivalued inverse of the functionw →we w. It has many applications in pure and applied mathematics, some of which are briefly described here. We present a new discussion of the complex branches ofW, an asymptotic expansion valid for all branches, an efficient numerical procedure for evaluating the function to arbitrary precision, and a method for the symbolic integration of expressions containingW.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Western Ontario, N6A 5B7, London, Canada

    R. M. Corless & D. J. Jeffrey

  2. Institut für Wissenschaftliches Rechnen, ETH, Zürich, Switzerland

    G. H. Gonnet

  3. Symbolic Computation Group, University of Waterloo, N2L 3G1, Waterloo, Canada

    D. E. G. Hare

  4. Department of Computer Science, Stanford University, 94305-2140, Stanford, California, USA

    D. E. Knuth

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  1. R. M. Corless
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  2. G. H. Gonnet
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  3. D. E. G. Hare
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  4. D. J. Jeffrey
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  5. D. E. Knuth
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Communicated by W.H. Enright

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Corless, R.M., Gonnet, G.H., Hare, D.E.G. et al. On the LambertW function. Adv Comput Math 5, 329–359 (1996). https://doi.org/10.1007/BF02124750

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