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LAMBERT W-FUNCTION

  • Lambert W function
  • Multivalued function in mathematics

    In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse

    Lambert W function

    Lambert W function

    Lambert_W_function

  • Lagrange inversion theorem
  • Formula for inverting a Taylor series

    inverse function of an analytic function. Lagrange inversion is a special case of the inverse function theorem. Suppose z is defined as a function of w by

    Lagrange inversion theorem

    Lagrange_inversion_theorem

  • Scheil equation
  • Metallurgical equation

    the Lambert W function, W ( x ) {\displaystyle W(x)} , which is defined as the inverse function of x = W ( x ) e W ( x ) {\displaystyle x=W(x)e^{W(x)}}

    Scheil equation

    Scheil equation

    Scheil_equation

  • Saturable absorption
  • Nonlinear optical effect

    (5)~~~~u=\omega (-t)} The solution can be expressed also through the related Lambert W function. Let u = V ( − e t ) {\displaystyle u=V{\big (}-\mathrm {e} ^{t}{\big

    Saturable absorption

    Saturable_absorption

  • Tetration
  • Arithmetic operation

    the Lambert W function: s s r t ( x ) = exp ⁡ ( W ( ln ⁡ x ) ) = ln ⁡ x W ( ln ⁡ x ) {\displaystyle \mathrm {ssrt} (x)=\exp(W(\ln x))={\frac {\ln x}{W(\ln

    Tetration

    Tetration

    Tetration

  • Omega constant
  • Solution to x * e^x = 1

    the value of W(1), where W is Lambert's W function. The name is derived from the alternate name for Lambert's W function, the omega function. The numerical

    Omega constant

    Omega_constant

  • Fox H-function
  • Generalization of the Meijer G-function and the Fox–Wright function

    in the numerator. A relation of the Fox H-Function to the -1 branch of the Lambert W-function is given by W − 1 ⁡ ( − α ⋅ z ) ¯ = { lim β → α − [ α 2

    Fox H-function

    Fox H-function

    Fox_H-function

  • Omega function
  • Topics referred to by the same term

    related to the Lambert W Function The Pearson–Cunningham function ω m , n ( x ) {\displaystyle \omega _{m,n}(x)} The prime omega function ω ( n ) {\displaystyle

    Omega function

    Omega_function

  • Darcy friction factor formulae
  • Equations for calculations of the Darcy friction factor

    usually solved numerically due to its implicit nature. Recently, the Lambert W function has been employed to obtain an exact solution in an explicit reformulation

    Darcy friction factor formulae

    Darcy_friction_factor_formulae

  • Logarithm
  • Mathematical function, inverse of an exponential function

    science), the Lambert W function, and the logit. They are the inverse functions of the double exponential function, tetration, of f(w) = wew, and of

    Logarithm

    Logarithm

    Logarithm

  • Wright omega function
  • Mathematical function

    mathematics, the Wright omega function or Wright function, denoted ω, is defined in terms of the Lambert W function as: ω ( z ) = W ⌈ I m ( z ) − π 2 π ⌉ (

    Wright omega function

    Wright omega function

    Wright_omega_function

  • List of mathematical functions
  • G-function Fox H-function Hyperoperations Iterated logarithm Super-logarithms Tetration Lambert W function: Inverse of f(w) = w exp(w). Lamé function Mathieu

    List of mathematical functions

    List_of_mathematical_functions

  • Elementary function
  • Type of mathematical function

    example, the Lambert function w = W ( z ) {\displaystyle w=W(z)} , which is defined implicitly by the equation ⁠ w e w = z {\displaystyle we^{w}=z} ⁠, has

    Elementary function

    Elementary_function

  • Johann Heinrich Lambert
  • Swiss polymath (1728–1777)

    Johann Heinrich Lambert (German: [ˈlambɛʁt]; French: Jean-Henri Lambert; 26 or 28 August 1728 – 25 September 1777) was a polymath from the Republic of

    Johann Heinrich Lambert

    Johann Heinrich Lambert

    Johann_Heinrich_Lambert

  • Equation xy = yx
  • In general, exponentiation fails to be commutative

    x = exp ⁡ ( − W ( x ) ) {\displaystyle W(x)/x=\exp(-W(x))} . Here we split the solution into the two branches of the Lambert W function and focus on each

    Equation xy = yx

    Equation xy = yx

    Equation_xy_=_yx

  • List of physical constants
  • the Lambert W function. b ′ = ( 3 + W 0 ( − 3 e − 3 ) ) k h {\displaystyle b'=\left(3+W_{0}\left(-3e^{-3}\right)\right){\frac {k}{h}}} , where W 0 {\displaystyle

    List of physical constants

    List_of_physical_constants

  • W (disambiguation)
  • Topics referred to by the same term

    abbreviation: W), an amino acid Haplogroup W (mtDNA), a human mitochondrial DNA (mtDNA) haplogroup W chromosome Lambert W function, a set of functions where w is

    W (disambiguation)

    W_(disambiguation)

  • W0
  • Topics referred to by the same term

    meteorites by weathering W0 may refer to the principal branch of the Lambert W Function 0W (disambiguation) This disambiguation page lists articles associated

    W0

    W0

  • Riemann zeta function
  • Analytic function in mathematics

    _{n=0}^{\infty }B_{n,\geq 2}^{(s)}{\frac {(W_{k}(-1))^{n}}{n!}},} where k ∈ {−1, 0}, Wk is the kth branch of the Lambert W-function, and B(μ) n,≥2 is an incomplete

    Riemann zeta function

    Riemann zeta function

    Riemann_zeta_function

  • Complex logarithm
  • Logarithm of a complex number

    It was first introduced in the paper Unwinding the Branches of the Lambert W function and was later referenced in the work of David Jeffrey. The argument

    Complex logarithm

    Complex logarithm

    Complex_logarithm

  • Transcendental number
  • In mathematics, a non-algebraic number

    Lindemann–Weierstrass theorem). W ( a ) {\displaystyle W(a)} if a is algebraic and nonzero, for any branch of the Lambert W function (by the Lindemann–Weierstrass

    Transcendental number

    Transcendental_number

  • Planck's law
  • Spectral density of light emitted by a black body

    {B} }T,} where W is the Lambert W function and e is Euler's number. However, the distribution Bλ peaks at a different energy E = [ 5 + W ( − 5 e − 5 )

    Planck's law

    Planck's law

    Planck's_law

  • Exponential function
  • Mathematical function, denoted exp(x) or e^x

    Half-exponential function, a compositional square root of an exponential function Lambert W function#Solving equations – Multivalued function in mathematics

    Exponential function

    Exponential function

    Exponential_function

  • Wien's displacement law
  • Relation between peak wavelengths of black body radiation and temperature

    = 5 + W 0 ( − 5 e − 5 ) {\displaystyle x=5+W_{0}(-5e^{-5})} where W 0 {\displaystyle W_{0}} is the principal branch of the Lambert W function, and gives

    Wien's displacement law

    Wien's displacement law

    Wien's_displacement_law

  • Michaelis–Menten kinetics
  • Model of enzyme kinetics

    of the Lambert W function. Namely, a K m = W ( F ( t ) ) {\displaystyle {\frac {a}{K_{\mathrm {m} }}}=W(F(t))} where W is the Lambert W function and F

    Michaelis–Menten kinetics

    Michaelis–Menten kinetics

    Michaelis–Menten_kinetics

  • Theory of solar cells
  • it can then be solved using the Lambert W function: I out = ( I L + I 0 ) − V out / R SH 1 + R S / R SH − n V T R S W ( I 0 R S n V T ( 1 + R S / R SH

    Theory of solar cells

    Theory of solar cells

    Theory_of_solar_cells

  • Euler's three-body problem
  • Problem in physics and astronomy

    (energies) have been obtained: these are a generalization of the Lambert W function. Various generalizations of Euler's problem are known; these generalizations

    Euler's three-body problem

    Euler's_three-body_problem

  • Darcy–Weisbach equation
  • Equation in fluid dynamics

    analytic function of Re through the use of the Lambert W function: 1 f D = 1.930 ln ⁡ ( 10 ) W ( 10 − 0.537 1.930 ln ⁡ ( 10 ) 1.930 R e ) = 0.838   W ( 0.629

    Darcy–Weisbach equation

    Darcy–Weisbach_equation

  • Lambert
  • Topics referred to by the same term

    hyperbolic functions in trigonometry and discovered Lambert's cosine law in optics. Lambert, Bishop of Ostia (c. 1036–1130), became Pope Honorius II Lambert, Margrave

    Lambert

    Lambert

  • Delta potential
  • Model of an energy potential in quantum mechanics

    problem, the solutions are given by a generalization of the Lambert W function (see Lambert W function § Generalizations). One of the most interesting cases

    Delta potential

    Delta_potential

  • Enzyme kinetics
  • Study of biochemical reaction rates catalysed by an enzyme

    the form: [ S ] K M = W [ F ( t ) ] {\displaystyle {\frac {[S]}{K_{M}}}=W\left[F(t)\right]\,} where W[ ] is the Lambert-W function and where F(t) is F (

    Enzyme kinetics

    Enzyme kinetics

    Enzyme_kinetics

  • Pranawachandra Deshmukh
  • Indian physicist, educator and administrator

    light–matter interactions, ultrafast atomic processes, and applications of Lambert W Function in pure and applied physics. He has made significant contributions

    Pranawachandra Deshmukh

    Pranawachandra Deshmukh

    Pranawachandra_Deshmukh

  • Economic order quantity
  • Production scheduling model

    of fuel injection in GDI engine using economic order quantity and Lambert W function". Applied Thermal Engineering. 101: 112–20. doi:10.1016/j.applthermaleng

    Economic order quantity

    Economic_order_quantity

  • Quadratrix of Hippias
  • Curve where spinning and moving lines cross

    equivalence between the quadratrix, the image of the Lambert W function, and the graph of the function y = x cot ⁡ x {\displaystyle y=x\cot x} . The discovery

    Quadratrix of Hippias

    Quadratrix of Hippias

    Quadratrix_of_Hippias

  • Gross tonnage
  • Nonlinear measure of a ship's overall internal volume

    ln {\displaystyle \ln } is the natural logarithm and W {\displaystyle W} is the Lambert W function. Transport portal Compensated gross tonnage List of

    Gross tonnage

    Gross tonnage

    Gross_tonnage

  • Inverse gamma function
  • Inverse of the gamma function

    }}}\right)}{W_{0}\left(e^{-1}\ln \left({\frac {x}{\sqrt {2\pi }}}\right)\right)}}\,,} where W 0 ( x ) {\displaystyle W_{0}(x)} is the Lambert W function. The

    Inverse gamma function

    Inverse gamma function

    Inverse_gamma_function

  • Black-body radiation
  • Thermal electromagnetic radiation

    2.897771955\times 10^{-3}\ {\mathsf {mK}},} and W 0 {\displaystyle W_{0}} is the Lambert W function. At a typical room temperature of 293 K (20 °C),

    Black-body radiation

    Black-body radiation

    Black-body_radiation

  • Lifting condensation level
  • Height at which an air parcel becomes saturated

    the parcel at its LCL. The function W − 1 {\displaystyle W_{-1}} is the − 1 {\displaystyle -1} branch of the Lambert W function. The best fit to empirical

    Lifting condensation level

    Lifting condensation level

    Lifting_condensation_level

  • Omega (disambiguation)
  • Topics referred to by the same term

    written as Ω Lambert W function, or omega function Omega constant, a specific value derived from the Lambert W function Wright omega function ω, the first

    Omega (disambiguation)

    Omega_(disambiguation)

  • Zero-inflated model
  • Statistical model allowing for frequent zero values

    H.; Hare, D. E. G.; Jeffrey, D. J.; Knuth, D. E. (1996). "On the Lambert W Function". Advances in Computational Mathematics. 5 (1): 329–359. arXiv:1809

    Zero-inflated model

    Zero-inflated_model

  • Kruskal–Szekeres coordinates
  • Coordinate system for the Schwarzschild geometry

    T^{2}-X^{2}<1} Using the Lambert W function the solution is written as: r = 2 G M ( 1 + W 0 ( X 2 − T 2 e ) ) . {\displaystyle r=2GM\left(1+W_{0}\left({\frac

    Kruskal–Szekeres coordinates

    Kruskal–Szekeres coordinates

    Kruskal–Szekeres_coordinates

  • Quantum chemistry
  • Chemistry based on quantum physics

    B-O approximation have been identified in terms of the generalized Lambert W function). Since all other atomic and molecular systems involve the motions

    Quantum chemistry

    Quantum chemistry

    Quantum_chemistry

  • Replica trick
  • Mathematical limit applied in statistical physics

    \end{aligned}}} Euler used a version of the replica trick in his study of the Lambert W function. S Edwards (1971), "Statistical mechanics of rubber". In Polymer networks:

    Replica trick

    Replica_trick

  • Trinomial
  • Polynomial that has three terms

    G. H.; Hare, D. E. G.; Jerey, D. J.; Knuth, D. E. (1996). "On the Lambert W Function" (PDF). Advances in Computational Mathematics. 5 (1): 329–359. doi:10

    Trinomial

    Trinomial

    Trinomial

  • Chernoff bound
  • Exponentially decreasing bounds on tail distributions of random variables

    {\displaystyle \delta =0} . In addition, based on the Taylor expansion for the Lambert W function, Pr ( X ≥ R ) ≤ 2 − x R , x > 0 ,   μ > 0 ,   R ≥ ( 2 x e − 1 ) μ

    Chernoff bound

    Chernoff_bound

  • Log-normal distribution
  • Probability distribution

    })}{2\sigma ^{2}}}\right)}{\sqrt {1+W{\left(-it\sigma ^{2}e^{\mu }\right)}}}}} where W {\displaystyle W} is the Lambert W function. This approximation is derived

    Log-normal distribution

    Log-normal distribution

    Log-normal_distribution

  • Binomial series
  • Mathematical series

    Binomial approximation Binomial theorem Table of Newtonian series Lambert W function In fact this source gives all non-constant terms with a negative sign

    Binomial series

    Binomial_series

  • Dihydrogen cation
  • Molecular ion

    the electronic energy eigenvalues are also a generalization of the Lambert W function which can be obtained using a computer algebra system within an experimental

    Dihydrogen cation

    Dihydrogen cation

    Dihydrogen_cation

  • Differentiation rules
  • Rules for computing derivatives of functions

    {x+e^{W(x)}}},\qquad x>-{1 \over e},} where W ( x ) {\textstyle W(x)} is the Lambert W function. d d x ( x x ) = x x ( 1 + ln ⁡ x ) . {\displaystyle {\frac

    Differentiation rules

    Differentiation_rules

  • Diode modelling
  • Any mathematical model describing semiconductor diodes

    using the Lambert W-function, which is the inverse function of f ( w ) = w e w {\displaystyle f(w)=we^{w}} , that is, w = W ( f ) {\displaystyle w=W(f)} .

    Diode modelling

    Diode_modelling

  • List of mathematical constants
  • numbers List of physical constants Particular values of the Riemann zeta function Physical constant Both i and −i are roots of this equation, though neither

    List of mathematical constants

    List_of_mathematical_constants

  • Frank-Kamenetskii theory
  • Scientific theory that explains thermal explosions

    where W {\displaystyle W} represents the Lambert W function. From the properties of Lambert W function, it is easy to see that the steady state temperature

    Frank-Kamenetskii theory

    Frank-Kamenetskii_theory

  • List of eponyms of special functions
  • polynomial Edmond Laguerre: Laguerre polynomials Johann Heinrich Lambert: Lambert W function Gabriel Lamé: Lamé polynomial G. Lauricella Lauricella-Saran:

    List of eponyms of special functions

    List_of_eponyms_of_special_functions

  • Gompertz–Makeham law of mortality
  • Mathematical equation related to human death rate

    using the principal branch W 0 {\displaystyle W_{0}} of the Lambert W function as Q ( u ) = α β λ − 1 λ ln ⁡ ( 1 − u ) − 1 β W 0 ( α λ exp [ α λ ] ( 1 −

    Gompertz–Makeham law of mortality

    Gompertz–Makeham law of mortality

    Gompertz–Makeham_law_of_mortality

  • Reciprocal gamma function
  • Mathematical function

    {1+z_{0}\ }}}\right)\ ,} where z0 = −1/n exp(W−1(−n)), and W−1 is the negative-first branch of the Lambert W function. The Taylor expansion around 1 has the

    Reciprocal gamma function

    Reciprocal gamma function

    Reciprocal_gamma_function

  • Widlar current source
  • Electronic circuit

    transcendental equations above can be solved exactly in terms of the Lambert W function. An important property of a current source is its small signal incremental

    Widlar current source

    Widlar current source

    Widlar_current_source

  • List of things named after Johann Lambert
  • Lambert summation Lambert W function Lambert's problem Lambert's theorem on the parabola Lambert's trinomial equation Lambertian function (inverse of the

    List of things named after Johann Lambert

    List_of_things_named_after_Johann_Lambert

  • Omega
  • Last letter of the Greek alphabet

    science: In complex analysis, the Omega constant, a solution of Lambert's W function. In differential geometry, the space of differential forms on a manifold

    Omega

    Omega

  • Compartmental models (epidemiology)
  • Type of mathematical model used for infectious diseases

    the Lambert W function, namely s ∞ = 1 − r ∞ = − R 0 − 1 W ( − s 0 R 0 e − R 0 ( 1 − r 0 ) ) . {\displaystyle s_{\infty }=1-r_{\infty }=-R_{0}^{-1}\,W

    Compartmental models (epidemiology)

    Compartmental_models_(epidemiology)

  • List of exponential topics
  • Gaussian function Gudermannian function Half-exponential function Half-life Hyperbolic function Inflation, inflation rate Interest Lambert W function Lifetime

    List of exponential topics

    List_of_exponential_topics

  • Holstein–Herring method
  • Numeric method in quantum chemistry

    molecular ion – Two hydrogen nuclei sharing one electron Lambert W function – Multivalued function in mathematics Quantum tunnelling – Quantum mechanical

    Holstein–Herring method

    Holstein–Herring_method

  • Transcendental equation
  • Equation whose side(s) describe a transcendental function

    solutions for y are known, those for x can be obtained by applying the Lambert W function,[citation needed] e.g.: x 2 e 2 x + 2 = 3 x e x {\displaystyle

    Transcendental equation

    Transcendental equation

    Transcendental_equation

  • Experimental mathematics
  • Approach to mathematics using computation

    same unique analytical solution in terms of a generalization of the Lambert W function. Related to this work is the isolation of a previously unknown link

    Experimental mathematics

    Experimental_mathematics

  • Latin letters used in mathematics, science, and engineering
  • entropy formula weight measured in newtons Lambert's W function Tungsten W boson Work function Wiener process w represents: the coordinate on the fourth

    Latin letters used in mathematics, science, and engineering

    Latin_letters_used_in_mathematics,_science,_and_engineering

  • Bell number
  • Count of the possible partitions of a set

    approximated using the Lambert W function, a function with the same growth rate as the logarithm, as B n ∼ 1 n ( n W ( n ) ) n + 1 2 exp ⁡ ( n W ( n ) − n − 1

    Bell number

    Bell number

    Bell_number

  • Projectile motion
  • Motion of launched objects due to gravity

    (}{\frac {t-t_{\mathrm {peak} }}{t_{f}}}{\biggr )})} With hyperbolic functions After a time t f {\displaystyle t_{f}} at y=0, the projectile reaches

    Projectile motion

    Projectile motion

    Projectile_motion

  • Delay differential equation
  • Type of differential equation

    given by λ = W k ( − 1 ) , {\displaystyle \lambda =W_{k}(-1),} where Wk is the kth branch of the Lambert W function, so: x ( t ) = x ( 0 ) e W k ( − 1 )

    Delay differential equation

    Delay_differential_equation

  • Edward W. Packel
  • 1016/0020-0255(92)90123-P. Packel, Edward W.; Yuen, David S. (2004). "Projectile Motion with Resistance and the Lambert W Function". The College Mathematics Journal

    Edward W. Packel

    Edward_W._Packel

  • Two-body problem in general relativity
  • bodies of equal masses can be solved analytically in terms of the Lambert W function. However, the gravitational energy between the two bodies is exchanged

    Two-body problem in general relativity

    Two-body_problem_in_general_relativity

  • Dilaton
  • Hypothetical particle

    was amenable to exact solutions in terms of a generalization of the Lambert W function. Also, the field equation governing the dilaton, derived from differential

    Dilaton

    Dilaton

  • Borel distribution
  • Probability distribution for branching processes

    result, the probability mass function is given by Pr ( W = n ) = k n e − μ n ( μ n ) n − k ( n − k ) ! {\displaystyle \Pr(W=n)={\frac {k}{n}}{\frac {e^{-\mu

    Borel distribution

    Borel_distribution

  • Galip Ulsoy
  • Turkish American academic (born 1950)

    Patrick W.; Ulsoy, A. Galip (April 2008). "Controllability and Observability of Systems of Linear Delay Differential Equations Via the Matrix Lambert W Function"

    Galip Ulsoy

    Galip Ulsoy

    Galip_Ulsoy

  • List of quantum-mechanical systems with analytical solutions
  • {r} ,t\right)}}{\partial t}},} where ψ {\displaystyle \psi } is the wave function of the system, H ^ {\displaystyle {\hat {H}}} is the Hamiltonian operator

    List of quantum-mechanical systems with analytical solutions

    List_of_quantum-mechanical_systems_with_analytical_solutions

  • Generating function
  • Formal power series

    various types of generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and Dirichlet

    Generating function

    Generating_function

  • Ross' π lemma
  • disturbances, the proportionality factor can be written in terms of the Lambert W-function. In practical applications, Ross' time constant can be found by numerical

    Ross' π lemma

    Ross'_π_lemma

  • Riemann–Siegel theta function
  • Mathematical function

    {1}{e}}\left(n+1-{\frac {7}{8}}\right)\right)}},} where W {\displaystyle W} is the Lambert W function. Here are the smallest non negative Gram points The

    Riemann–Siegel theta function

    Riemann–Siegel_theta_function

  • Zero-truncated Poisson distribution
  • Conditional Poisson distribution restricted to positive integers

    is the sample mean. This equation has a solution in terms of the Lambert W function. In practice, a solution may be found using numerical methods. Imagine

    Zero-truncated Poisson distribution

    Zero-truncated_Poisson_distribution

  • Gaisser–Hillas function
  • Function in physics to determine particle density

    Press. ISBN 978-0-08-016724-4. 2013 edition Darko Veberič (2012). "Lambert W Function for Applications in Physics". Computer Physics Communications. 183

    Gaisser–Hillas function

    Gaisser–Hillas_function

  • Edmond–Ogston model
  • positive. The spinodal can be expressed analytically too, and the Lambert W function has a central role to express the coordinates of binodal and tie-lines

    Edmond–Ogston model

    Edmond–Ogston_model

  • Sullivan vortex
  • Solution to the Navier–Stokes equations

    _{s}-3)]} where W 0 {\displaystyle W_{0}} is the principal branch of the Lambert W function. Thus, r s {\displaystyle r_{s}} here should be interpreted as the

    Sullivan vortex

    Sullivan vortex

    Sullivan_vortex

  • Equation solving
  • Finding values for variables that make an equation true

    inverse functions include the nth root (inverse of xn); the logarithm (inverse of ax); the inverse trigonometric functions; and Lambert's W function (inverse

    Equation solving

    Equation solving

    Equation_solving

  • Benktander type II distribution
  • Distribution introduced by Gunnar Benktander

    non-life/casualty actuarial science, using various forms of mean excess functions (Benktander & Segerdahl 1960). This distribution is "close" to the Weibull

    Benktander type II distribution

    Benktander type II distribution

    Benktander_type_II_distribution

  • Hyperbolic functions
  • Hyperbolic analogues of trigonometric functions

    hyperbolic functions using the imaginary unit and extended de Moivre's formula to hyperbolic functions. During the 1760s, Johann Heinrich Lambert systematized

    Hyperbolic functions

    Hyperbolic functions

    Hyperbolic_functions

  • Trigonometric functions
  • Functions of an angle

    mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of

    Trigonometric functions

    Trigonometric functions

    Trigonometric_functions

  • Wu–Sprung potential
  • Concept in mathematical physics

    π 2 n 2 W 2 ( n e − 1 ) {\textstyle E_{n}={\frac {4\pi ^{2}n^{2}}{W^{2}(ne^{-1})}}} , where W is the Lambert W function. Wu, Hua; Sprung, D. W. L. (1993)

    Wu–Sprung potential

    Wu–Sprung_potential

  • Lambert series
  • Mathematical term

    number-theoretic sum, almost any natural multiplicative function will be exactly summable when used in a Lambert series. Thus, for example, one has ∑ n = 1 ∞ q

    Lambert series

    Lambert series

    Lambert_series

  • Gudermannian function
  • Mathematical function relating circular and hyperbolic functions

    Johann Heinrich Lambert, and later named for Christoph Gudermann who also described the relationship between circular and hyperbolic functions in 1830. The

    Gudermannian function

    Gudermannian function

    Gudermannian_function

  • Theta function
  • Special functions of several complex variables

    Value". msu.edu. Retrieved 2023-04-07. Ramanujan's theta-function identities involving Lambert series "code golf - Strict partitions of a positive integer"

    Theta function

    Theta function

    Theta_function

  • Jacobi elliptic functions
  • Mathematical function

    ( 2 K ( m ) ) {\displaystyle v=\pi u/(2K(m))} . Then the functions have expansions as Lambert series am ⁡ ( u , m ) = π u 2 K ( m ) + 2 ∑ n = 1 ∞ q n n

    Jacobi elliptic functions

    Jacobi_elliptic_functions

  • Möbius function
  • Multiplicative function in number theory

    where γ {\displaystyle \gamma } is Euler's constant. The Lambert series for the Möbius function is ∑ n = 1 ∞ μ ( n ) q n 1 − q n = q , {\displaystyle \sum

    Möbius function

    Möbius_function

  • Euler's totient function
  • Number of integers coprime to and less than n

    converges for ℜ ( s ) > 2 {\displaystyle \Re (s)>2} . The Lambert series generating function is ∑ n = 1 ∞ φ ( n ) q n 1 − q n = q ( 1 − q ) 2 {\displaystyle

    Euler's totient function

    Euler's totient function

    Euler's_totient_function

  • Eva Braun
  • Wife of Adolf Hitler (1912–1945)

    corpse's tongue. Lambert 2006, p. 46. Lambert 2006, p. 55. Görtemaker 2011, p. 31. Lambert 2006, p. 17. Görtemaker 2011, pp. 31–32. Lambert 2006, pp. 49,

    Eva Braun

    Eva Braun

    Eva_Braun

  • Pores of Kohn
  • Discrete holes in the wall of the lungs that aide in movement of cells and pathogens

    human newborns. They develop at 3–4 years of age along with canals of Lambert during the process of thinning of alveolar septa. The pores allow the passage

    Pores of Kohn

    Pores_of_Kohn

  • Divisor function
  • Arithmetic function related to the divisors of an integer

    theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as the divisor function, it counts the number

    Divisor function

    Divisor function

    Divisor_function

  • Transverse Mercator projection
  • Adaptation of the standard Mercator projection

    presented, in 1772, by Johann Heinrich Lambert. (The text is also available in a modern English translation.) Lambert did not name his projections; the name

    Transverse Mercator projection

    Transverse Mercator projection

    Transverse_Mercator_projection

  • Closed-form expression
  • Mathematical formula involving a given set of operations

    (2018). "Siewert solutions of transcendental equations, generalized Lambert functions and physical applications". Open Physics. 16 (1). De Gruyter: 232–242

    Closed-form expression

    Closed-form_expression

  • Particular values of the Riemann zeta function
  • Constants of the mathematical zeta function

    In mathematics, the Riemann zeta function is a function in complex analysis, which is also important in number theory. It is often denoted ζ ( s ) {\displaystyle

    Particular values of the Riemann zeta function

    Particular values of the Riemann zeta function

    Particular_values_of_the_Riemann_zeta_function

  • Polylogarithm
  • Special mathematical function

    }\qquad (n=1,2,3,\ldots ).} Using Lambert series, if J s ( n ) {\displaystyle J_{s}(n)} is Jordan's totient function, then ∑ n = 1 ∞ z n J − s ( n ) 1

    Polylogarithm

    Polylogarithm

    Polylogarithm

  • Neuromuscular junction disease
  • Medical condition

    myasthenia gravis, and Lambert-Eaton syndrome.(reference 26) In each of these diseases, a receptor or other protein essential to normal function of the junction

    Neuromuscular junction disease

    Neuromuscular_junction_disease

  • Reinforcement learning from human feedback
  • Machine learning technique

    cross-entropy loss function: L ( θ ) = − 1 ( K 2 ) E ( x , y w , y l ) [ log ⁡ ( σ ( r θ ( x , y w ) − r θ ( x , y l ) ) ) ] = − 1 ( K 2 ) E ( x , y w , y l ) log

    Reinforcement learning from human feedback

    Reinforcement learning from human feedback

    Reinforcement_learning_from_human_feedback

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  • Lambirth
  • Surname or Lastname

    English

    Lambirth

    English : probably a variant of Lambert. Compare Lamberth.

    Lambirth

  • Amber
  • Girl/Female

    Muslim American Arabic English Gaelic

    Amber

    Jewel. Amber stone.

    Amber

  • Lampert
  • Surname or Lastname

    English, North German, and Hungarian (Lampért)

    Lampert

    English, North German, and Hungarian (Lampért) : variant of Lambert.

    Lampert

  • Lamberth
  • Surname or Lastname

    English

    Lamberth

    English : probably a variant of Lambert.

    Lamberth

  • Lambert
  • Surname or Lastname

    English, French, Dutch, and German

    Lambert

    English, French, Dutch, and German : from a Germanic personal name composed of the elements land ‘land’, ‘territory’ + berht ‘bright’, ‘famous’. In England, the native Old English form Landbeorht was replaced by Lambert, the Continental form of the name that was taken to England by the Normans from France. The name gained wider currency in Britain in the Middle Ages with the immigration of weavers from Flanders, among whom St. Lambert or Lamprecht, bishop of Maastricht in around 700, was a popular cult figure. In Italy the name was popularized in the Middle Ages as a result of the fame of Lambert I and II, Dukes of Spoleto and Holy Roman Emperors.The name Lambert is found in Quebec City from 1657, taken there from Picardy, France. There are also Lamberts from Perche, France, by 1670.

    Lambert

  • HUMBERT
  • Male

    English

    HUMBERT

    English form of Norman Germanic Huncberct, possibly HUMBERT means "bright support." 

    HUMBERT

  • Lamport
  • Surname or Lastname

    English

    Lamport

    English : probably a variant of Lambert.

    Lamport

  • RAIBERT
  • Male

    Scottish

    RAIBERT

    Variant spelling of Scottish Gaelic Raibeart, RAIBERT means "bright fame."

    RAIBERT

  • ALBERT
  • Male

    English

    ALBERT

     Middle English form of Anglo-Saxon Æthelbert, ALBERT means "bright nobility." Compare with other forms of Albert.

    ALBERT

  • LAMMERT
  • Male

    French

    LAMMERT

    Low German form of Germanic Landebert, LAMMERT means "land-bright." In use by the Dutch and French.

    LAMMERT

  • BAMBER
  • Male

    German

    BAMBER

    German byname BAMBER means "short and fat." 

    BAMBER

  • Lambert
  • Boy/Male

    German American Teutonic

    Lambert

    Bright land. Can be used as both a surname and first name. Famous Bearer: Belgian-American...

    Lambert

  • Lambert
  • Boy/Male

    American, Australian, British, Christian, Danish, Dutch, English, Finnish, French, German, Polish, Swedish, Teutonic

    Lambert

    Famous Landowner; Brightness of the Land; Land

    Lambert

  • LUBBERT
  • Male

    German

    LUBBERT

    German surname transferred to forename use, derived from the personal name Liutbert, LUBBERT means "people-bright."

    LUBBERT

  • ALBERT
  • Male

    French

    ALBERT

     French name derived from Latin Albertus, ALBERT means "bright nobility." Compare with other forms of Albert.

    ALBERT

  • Lammert
  • Surname or Lastname

    English and North German (also Lämmert)

    Lammert

    English and North German (also Lämmert) : variant of Lambert.

    Lammert

  • LAMBERT
  • Male

    English

    LAMBERT

    Middle English form of Low German Lammert, LAMBERT means "land-bright."

    LAMBERT

  • Calbert
  • Surname or Lastname

    English

    Calbert

    English : variant of Albert, probably due to misdivision of a personal name such as Rick Albert.

    Calbert

  • AUBERT
  • Male

    French

    AUBERT

    French form of Old High German Adalbert, AUBERT means "bright nobility."

    AUBERT

  • LAMBART
  • Male

    English

    LAMBART

    Variant form of English Lambert, LAMBART means "land-bright."

    LAMBART

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Online names & meanings

  • Duling
  • Surname or Lastname

    English (Kent)

    Duling

    English (Kent) : unexplained.Possibly an altered spelling of the German surname Dulling, which is likewise unexplained.

  • Meeksha | மிக்ஷா
  • Girl/Female

    Tamil

    Meeksha | மிக்ஷா

  • Henrik
  • Boy/Male

    Danish, Finnish, French, German, Hindu, Indian, Slovenia, Swedish

    Henrik

    Form of Henry; Ruler of the Home; House Owner; Lord of the Manor; Ruler of an Enclosure

  • DIKELEDI
  • Female

    African

    DIKELEDI

    tears.

  • Nilavoli
  • Girl/Female

    Assamese, Hindu, Indian, Kannada, Marathi, Sindhi, Tamil, Telugu

    Nilavoli

    Ray of Light from the Moon

  • Salah Al Din |
  • Boy/Male

    Muslim

    Salah Al Din |

    Righteousness of the faith, Name of the Muslim leader who liberated jerusalem from the crusaders

  • Veesta
  • Girl/Female

    Indian

    Veesta

    Finder

  • Namdev
  • Boy/Male

    Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Punjabi, Sikh, Sindhi, Telugu

    Namdev

    Lord Vishnu; Poet; Saint; A Godly Person

  • Branigan
  • Boy/Male

    Irish

    Branigan

    Surname.

  • Rodney
  • Boy/Male

    Christian & English(British/American/Australian)

    Rodney

    Famous

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Other words and meanings similar to

LAMBERT W-FUNCTION

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  • Lamented
  • imp. & p. p.

    of Lament

  • Lumber
  • b. t.

    To fill or encumber with lumber; as, to lumber up a room.

  • Clambering
  • p. pr. & vb. n.

    of Clamber

  • Amber
  • a.

    Consisting of amber; made of amber.

  • Cambered
  • imp. & p. p.

    of Camber

  • Limber
  • v. t.

    To attach to the limber; as, to limber a gun.

  • Limbered
  • imp. & p. p.

    of Limber

  • Cambering
  • p. pr. & vb. n.

    of Camber

  • Amber
  • a.

    Resembling amber, especially in color; amber-colored.

  • Camber
  • n.

    An upward convexity of a deck or other surface; as, she has a high camber (said of a vessel having an unusual convexity of deck).

  • Limbering
  • p. pr. & vb. n.

    of Limber

  • Clambered
  • imp. & p. p.

    of Clamber

  • Lumbered
  • imp. & p. p.

    of Lumber

  • Amber
  • v. t.

    To preserve in amber; as, an ambered fly.

  • Lumbering
  • p. pr. & vb. n.

    of Lumber

  • Limmer
  • a.

    Limber.

  • Amber
  • n.

    Amber color, or anything amber-colored; a clear light yellow; as, the amber of the sky.

  • Limber
  • v. t.

    To cause to become limber; to make flexible or pliant.

  • Lamenting
  • p. pr. & vb. n.

    of Lament