A Brief Look into the Lambert W Function

Dence, Thomas P.

doi:10.4236/am.2013.46122

Cited by 49 publications

(23 citation statements)

References 15 publications

(18 reference statements)

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“…Since then, many works have appeared with reviews and significant contributions to the approximation of the ( ) oriented to diverse applications; some relevant works are presented by Corless et al [21,22], Brito et al [6], Abdolhossein et al [23], Fukushima [24], Marko [25], Fredrik [9], Jeffrey et al [26], Jeffrey [27], Kheyfits [28], Darko [7], Dence [29], and Mezo et al [30]. Moreover, a conference was created and celebrated in honour of the Lambert W Function in 2016.…”

Section: = +mentioning

confidence: 99%

PSEM Approximations for Both Branches of Lambert W Function with Applications

Vázquez-Leal

Sandoval-Hernandez

Garcia-Gervacio

et al. 2019

Discrete Dynamics in Nature and Society

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Transcendental functions are a fundamental building block of science and engineering. Among them, a relatively new function denominated as Lambert W is highlighted. The importance of such function relies on the fact that it can perform novel isolation of variables. In this work, we propose two accurate piece-wise approximate solutions, one for the lower branch and another one for the upper branch, respectively. The proposed analytic approximations are obtained by using the power series extender method (PSEM) in combination with asymptotic solutions. In addition, we will compare some published approximations with our proposal, highlighting our advantages in terms of significant digits and speed of evaluation. Furthermore, the approximations are validated by the successful simulation of a problem of economy and other acoustic waves of nonlinear ions.

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Section: = +mentioning

confidence: 99%

PSEM Approximations for Both Branches of Lambert W Function with Applications

Vázquez-Leal

Sandoval-Hernandez

Garcia-Gervacio

et al. 2019

Discrete Dynamics in Nature and Society

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“…is the Lambert function [29], which solves W [y]e W [y] = x. We have a non-degenerate horizon for |q| √ e/2 < m, then g 11 (r) = 0 has two real and different roots; for m = |q| √ e/2 we have a degenerate horizon, and g 11 (r) = 0 has a single real root; finally we have no horizon in the case |q| √ e/2 > m and g 11 (r) = 0 has no real root.…”

Section: Fixing A(r)mentioning

confidence: 99%

Regular black holes inf(T) Gravity through a nonlinear electrodynamics source

Ednaldo

Rodrigues

Houndjo

2015

J. Cosmol. Astropart. Phys.

102

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Abstract. We seek to obtain a new class of exact solutions of regular black holes in f (T ) Gravity with non-linear electrodynamics material content, with spherical symmetry in 4D. The equations of motion provide the regaining of various solutions of General Relativity, as a particular case where the function f (T ) = T . We developed a powerful method for finding exact solutions, where we get the first new class of regular black holes solutions in the f (T ) Theory, where all the geometrics scalars disappear at the origin of the radial coordinate and are finite everywhere, as well as a new class of singular black holes.

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“…A test is performed on the u * band of SDSS as in [43] with data available at https://cosmo.nyu.edu/ blanton/lf.html. The Schechter function, the new Lindley LF represented by formula (33) and the data are reported in Figure 5, parameters as in Table 3.…”

Section: The Lindley Lfmentioning

confidence: 99%

The Truncated Lindley Distribution with Applications in Astrophysics

Zaninetti¹

2019

Galaxies

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This paper reviews the Lindley distribution and then introduces the scale and the double truncation. The unknown parameters of the truncated Lindley distribution are evaluated with the maximum likelihood estimators. An application of the Lindley distribution with scale is done to the initial mass function for stars. The magnitude version of the Lindley distribution with scale is applied to the luminosity function for the Sloan Digital Sky Survey (SDSS) galaxies and to the photometric maximum of the 2MASS Redshift Survey (2MRS) galaxies. The truncated Lindley luminosity function allows us to model the Malquist bias of the 2MRS galaxies.

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A Brief Look into the Lambert W Function

Abstract: The Lambert W function has its origin traced back 250 years, but it's just been in the past several decades when some of the real usefulness of the function has been brought to the attention of the scientific community.

Cited by 49 publications

References 15 publications

PSEM Approximations for Both Branches of Lambert W Function with Applications

PSEM Approximations for Both Branches of Lambert W Function with Applications

Regular black holes inf(T) Gravity through a nonlinear electrodynamics source

The Truncated Lindley Distribution with Applications in Astrophysics

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