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- Lambert_W_function abstract "In mathematics, the Lambert W function, also called the omega function or product logarithm, is a set of functions, namely the branches of the inverse relation of the function z = f(W) = WeW where eW is the exponential function and W is any complex number. In other words, the defining equation for W(z) is for any complex number z.Since the function ƒis not injective, the relation W is multivalued (except at 0). If we restrict attention to real-valued W, the complex variable z is then replaced by the real variable x, and the relation is defined only for x ≥ −1/e, and is double-valued on (−1/e, 0). The additional constraint W ≥ −1 defines a single-valued function W0(x). We have W0(0) = 0 and W0(−1/e) = −1. Meanwhile, the lower branch has W ≤ −1 and is denoted W−1(x). It decreases from W−1(−1/e) = −1 to W−1(0−) = −∞.The Lambert W relation cannot be expressed in terms of elementary functions. It is useful in combinatorics, for instance in the enumeration of trees. It can be used to solve various equations involving exponentials (e.g. the maxima of the Planck, Bose–Einstein, and Fermi–Dirac distributions) and also occurs in the solution of delay differential equations, such as y'(t) = a y(t − 1).↑".
- Lambert_W_function thumbnail Lambert-w.svg?width=300.
- Lambert_W_function wikiPageExternalLink 1003.1628.
- Lambert_W_function wikiPageExternalLink 2214.
- Lambert_W_function wikiPageExternalLink 4.13.
- Lambert_W_function wikiPageExternalLink ?id=EJ720055.
- Lambert_W_function wikiPageExternalLink EJ720055.pdf.
- Lambert_W_function wikiPageExternalLink math.
- Lambert_W_function wikiPageExternalLink LambertW-Function.html.
- Lambert_W_function wikiPageExternalLink why-w.
- Lambert_W_function wikiPageExternalLink W-adv-cm.pdf.
- Lambert_W_function wikiPageExternalLink LambertW.
- Lambert_W_function wikiPageExternalLink gsl.
- Lambert_W_function wikiPageExternalLink Lambert-W-Functions.html.
- Lambert_W_function wikiPageExternalLink Special-Functions.html.
- Lambert_W_function wikiPageExternalLink lambertw.pdf.
- Lambert_W_function wikiPageExternalLink view.aspx?path=LambertW.
- Lambert_W_function wikiPageExternalLink LambertW.
- Lambert_W_function wikiPageExternalLink lambertw.html.
- Lambert_W_function wikiPageID "92465".
- Lambert_W_function wikiPageRevisionID "605916439".
- Lambert_W_function first "F. W. J.".
- Lambert_W_function first "R.".
- Lambert_W_function hasPhotoCollection Lambert_W_function.
- Lambert_W_function id "4.13".
- Lambert_W_function last "Olver".
- Lambert_W_function last "Roy".
- Lambert_W_function title "Lambert W function".
- Lambert_W_function subject Category:Special_functions.
- Lambert_W_function type Abstraction100002137.
- Lambert_W_function type Function113783816.
- Lambert_W_function type MathematicalRelation113783581.
- Lambert_W_function type Relation100031921.
- Lambert_W_function type SpecialFunctions.
- Lambert_W_function comment "In mathematics, the Lambert W function, also called the omega function or product logarithm, is a set of functions, namely the branches of the inverse relation of the function z = f(W) = WeW where eW is the exponential function and W is any complex number. In other words, the defining equation for W(z) is for any complex number z.Since the function ƒis not injective, the relation W is multivalued (except at 0).".
- Lambert_W_function label "Fonction W de Lambert".
- Lambert_W_function label "Función W de Lambert".
- Lambert_W_function label "Funkcja W Lamberta".
- Lambert_W_function label "Funzione W di Lambert".
- Lambert_W_function label "Função W de Lambert".
- Lambert_W_function label "Lambert W function".
- Lambert_W_function label "Lambertsche W-Funktion".
- Lambert_W_function label "W-функция Ламберта".
- Lambert_W_function label "ランベルトのW関数".
- Lambert_W_function label "朗伯W函数".
- Lambert_W_function sameAs Lambertsche_W-Funktion.
- Lambert_W_function sameAs Función_W_de_Lambert.
- Lambert_W_function sameAs Fonction_W_de_Lambert.
- Lambert_W_function sameAs Funzione_W_di_Lambert.
- Lambert_W_function sameAs ランベルトのW関数.
- Lambert_W_function sameAs 람베르트_W_함수.
- Lambert_W_function sameAs Funkcja_W_Lamberta.
- Lambert_W_function sameAs Função_W_de_Lambert.
- Lambert_W_function sameAs m.0m_5j.
- Lambert_W_function sameAs Q429331.
- Lambert_W_function sameAs Q429331.
- Lambert_W_function sameAs Lambert_W_function.
- Lambert_W_function wasDerivedFrom Lambert_W_function?oldid=605916439.
- Lambert_W_function depiction Lambert-w.svg.
- Lambert_W_function isPrimaryTopicOf Lambert_W_function.
