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

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...

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)}}...

(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...

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...

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...

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...

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...

the Lambert W function. Some examples of functions that are not elementary: tetration the gamma function non-elementary Liouvillian functions, including...

Meijer G-function Fox H-function Hyper operators Iterated logarithm Pentation Super-logarithms Tetration Lambert W function: Inverse of f(w) = w exp(w). Lamé...

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...

{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 )...

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...

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

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...

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 ⌉ (...

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...

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

_{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...

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

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...

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...

= 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...

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...

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

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...

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...

German/Italian wine grape Trollinger Lambert v. California, court case regarding legal notice Lambert W function, mathematical definition of a product...

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

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...