Topic
Lambert W function
About: Lambert W function is a research topic. Over the lifetime, 713 publications have been published within this topic receiving 17799 citations. The topic is also known as: product logarithm & omega function.
Papers published on a yearly basis
Papers
TL;DR: A new discussion of the complex branches of W, 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 containing W are presented.
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.
6,474 citations
TL;DR: In this article, an exact closed-form solution based on Lambert W -function is presented to express the transcendental currentvoltage characteristic containing parasitic power consuming parameters like series and shunt resistances.
541 citations
1 Apr 2008
TL;DR: The h(t) solution, as it includes the gravity term (hydrostatic pressure), enables the calculation of the liquid rise behavior for longer times than the classical Lucas-Washburn equation.
Abstract: We derive an analytic solution for the capillary rise of liquids in a cylindrical tube or a porous medium in terms of height h as a function of time t. The implicit t(h) solution by Washburn is the basis for these calculations and the Lambert W function is used for its mathematical rearrangement. The original equation is derived out of the 1D momentum conservation equation and features viscous and gravity terms. Thus our h(t) solution, as it includes the gravity term (hydrostatic pressure), enables the calculation of the liquid rise behavior for longer times than the classical Lucas-Washburn equation. Based on the new equation several parameters like the steady state time and the validity of the Lucas-Washburn equation are examined. The results are also discussed in dimensionless form.
380 citations
TL;DR: In this paper, two standard physics problems are solved in terms of the Lambert W − function, to show the applicability of this recently defined function to physics, and the problems solved concern Wien's displacement law and the fringing fields of a capacitor, the latter problem being representative of some problems solved using conformal transformations.
Abstract: Two standard physics problems are solved in terms of the Lambert W function, to show the applicability of this recently defined function to physics. Other applications of the function are cited, but not described. The problems solved concern Wien's displacement law and the fringing fields of a capacitor, the latter problem being representative of some problems solved using conformal transformations. The physical content of the solutions remains unchanged, but they gain a new elegance and convenience. PACS No.: 41.10F
315 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 11 |
| 2024 | 20 |
| 2023 | 25 |
| 2022 | 41 |
| 2021 | 59 |
| 2020 | 58 |