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The notation convention chosen here (with W 0 and W −1) follows the canonical reference on the Lambert W function by Corless, Gonnet, Hare, Jeffrey and Knuth. [3]The name "product logarithm" can be understood as follows: since the inverse function of f(w) = e w is termed the logarithm, it makes sense to call the inverse "function" of the product we w the "product logarithm".
The Lambert W function is the function () that is implicitly defined by the equation W ( z ) e W ( z ) = z . {\displaystyle W(z)e^{W(z)}=z.} We may use the theorem to compute the Taylor series of W ( z ) {\displaystyle W(z)} at z = 0. {\displaystyle z=0.}
Taylor series are used to define functions and "operators" in diverse areas of mathematics. In particular, this is true in areas where the classical definitions of functions break down. For example, using Taylor series, one may extend analytic functions to sets of matrices and operators, such as the matrix exponential or matrix logarithm.
The test functions used to evaluate the algorithms for MOP were taken from Deb, [4] Binh et al. [5] and Binh. [6] The software developed by Deb can be downloaded, [ 7 ] which implements the NSGA-II procedure with GAs, or the program posted on Internet, [ 8 ] which implements the NSGA-II procedure with ES.
Johann Heinrich Lambert: Lambert W function; Gabriel Lamé: Lamé polynomial; G. Lauricella Lauricella-Saran: Lauricella hypergeometric series; Adrien-Marie Legendre: Legendre polynomials; Eugen Cornelius Joseph von Lommel (1837–1899), physicist: Lommel polynomial, Lommel function, Lommel–Weber function
There are various types of generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and Dirichlet series. Every sequence in principle has a generating function of each type (except that Lambert and Dirichlet series require indices to start at 1 rather than 0), but the ease ...
Adam Lambert stopped by Z100 to give a quick interview about his new album, The Original High.. During the fun, informative chat, the host pointed out that Lambert has gotten a few awards, and he ...
One problem with p/m or +/- is that it is limited to only two branches, but the numerical subscript allows indexing all branches of the Lambert W function (this article fails to note this). The "old" notation is also used in computer algebra systems, which are the most important domain of use for the Lambert W function.