Transformation that defines the Lambert W function and its derivative

Description

The Lambert W function W(z) is the inverse of u exp(u) = z.

In versions < 0.6.0 of the package this function was denoted as H. It is now replaced with the more descriptive xexp (and H is deprecated).

Usage

xexp(x)

deriv_xexp(x, degree = 1)

Arguments

Details

The n-th derviative of x cdot exp(x) is available in closed for as

exp(x) cdot (x + n).

Value

Returns z = x exp(x) for x in C. If x is a vector/matrix, so is z.

See Also

W

Examples

plot(xexp, -5, 0.5, type="l", xlab="u", ylab="z")
grid()
abline(h=0, lty = 2)
abline(v=0, lty = 2)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
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R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(LambertW)
Loading required package: MASS
Loading required package: ggplot2
This is 'LambertW' version 0.6.4.  Please see the NEWS file and citation("LambertW").

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/LambertW/xexp.Rd_%03d_medium.png", width=480, height=480)
> ### Name: xexp
> ### Title: Transformation that defines the Lambert W function and its
> ###   derivative
> ### Aliases: deriv_xexp xexp
> ### Keywords: math
> 
> ### ** Examples
> 
> 
> plot(xexp, -5, 0.5, type="l", xlab="u", ylab="z")
> grid()
> abline(h=0, lty = 2)
> abline(v=0, lty = 2)
> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>