Lambert W-function
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1: 4.13 Lambert -Function
§4.13 Lambert -Function
►The Lambert -function is the solution of the equation … ►We call the increasing solution for which the principal branch and denote it by . … ►The other branches are single-valued analytic functions on , have a logarithmic branch point at , and, in the case , have a square root branch point at respectively. … ►Properties include: …2: 4.44 Other Applications
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►For applications of generalized exponentials and generalized logarithms to computer arithmetic see §3.1(iv).
►For an application of the Lambert
-function to generalized Gaussian noise see Chapeau-Blondeau and Monir (2002).
For other applications of the Lambert
-function see Corless et al. (1996).
3: 28.8 Asymptotic Expansions for Large
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28.8.9
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4: 26.7 Set Partitions: Bell Numbers
5: 27.7 Lambert Series as Generating Functions
6: 4.48 Software
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►Links to research literature for the Lambert
-function and for test software are included also.
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§4.48(iv) Lambert -Function
…7: 4.45 Methods of Computation
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§4.45(iii) Lambert -Function
►For the principal branch can be computed by solving the defining equation numerically, for example, by Newton’s rule (§3.8(ii)). … ►Similarly for in the interval (with in (4.13.6)). …8: 4.1 Special Notation
9: 25.18 Methods of Computation
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►For dilogarithms and polylogarithms see Jacobs and Lambert (1972), Osácar et al. (1995), Spanier and Oldham (1987, pp. 231–232), and Zudilin (2007).
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10: Bibliography J
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On the numerical calculation of polylogarithms.
Nordisk Tidskr. Informationsbehandling (BIT) 12 (4), pp. 581–585.
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Stirling Numbers, Lambert W and the Gamma Function.
In Mathematical Aspects of Computer and Information Sciences, J. Blömer, I. S. Kotsireas, T. Kutsia, and D. E. Simos (Eds.),
Cham, pp. 275–279.
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