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 solution for which the principal branch and denote it by . … ►Properties include: … ►For integral representations of all branches of the Lambert -function see Kheyfits (2004). …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: 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 . …4: 27.7 Lambert Series as Generating Functions
5: 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
…6: 33.22 Particle Scattering and Atomic and Molecular Spectra
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►For bound-state problems only the exponentially decaying solution is required, usually taken to be the Whittaker function
.
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7: 26.7 Set Partitions: Bell Numbers
8: 12.19 Tables
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Fox (1960) includes modulus and phase functions for and , and several auxiliary functions for , , 8S.
9: 4.1 Special Notation
10: 28.8 Asymptotic Expansions for Large
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28.8.9
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