Lambert%20W-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
…
►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
4: 27.7 Lambert Series as Generating Functions
5: 4.48 Software
…
►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: 26.7 Set Partitions: Bell Numbers
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 . …8: Bibliography K
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Unimodal sequences show that Lambert
is Bernstein.
C. R. Math. Acad. Sci. Soc. R. Can. 33 (2), pp. 50–56.
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Bernstein, Pick, Poisson and related integral expressions for Lambert
.
Integral Transforms Spec. Funct. 23 (11), pp. 817–829.
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Closed-form representations of the Lambert
function.
Fract. Calc. Appl. Anal. 7 (2), pp. 177–190.
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