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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".
2 Example. 3 Applications. ... in the Taylor series of a function of w. ... The Lambert W function is the function () that is implicitly ...
This is a list of special function eponyms in ... Paul Émile Appell (1855–1930): Appell hypergeometric series, ... Johann Heinrich Lambert: Lambert W function;
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.
For example, the log-normal function with such fits well with the size of secondarily produced droplets during droplet impact [56] and the spreading of an epidemic disease. [ 57 ] The value σ = 1 / 6 {\textstyle \sigma =1{\big /}{\sqrt {6}}} is used to provide a probabilistic solution for the Drake equation.
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 ...
Function () = =, represented as a Matplotlib plot, using a version of the domain coloring method [1]. In mathematics, a Lambert series, named for Johann Heinrich Lambert, is a series taking the form
The inverse gamma function also has the following asymptotic formula [7] + ( ()), where () is the Lambert W function. The formula is found by inverting the Stirling approximation , and so can also be expanded into an asymptotic series.