# glog: Compute Generalized Logarithm In stamats/MKmisc: Miscellaneous Functions from M. Kohl

## Description

The functions compute the generalized logarithm, which is more or less identical to the area hyperbolic sine, and their inverse; see details.

## Usage

 ```1 2 3 4 5 6``` ```glog(x, base = exp(1)) glog10(x) glog2(x) inv.glog(x, base = exp(1)) inv.glog10(x) inv.glog2(x) ```

## Arguments

 `x` a numeric or complex vector. `base` a positive or a positive or complex number: the base with respect to which logarithms are computed. Defaults to e=exp(1).

## Details

The function computes

log(x + sqrt(x^2 + 1)) - log(2)

where the first part corresponds to the area hyperbolic sine. Subtracting log(2) makes the function asymptotically identical to the logarithm.

## Value

A vector of the same length as x containing the transformed values.

## Author(s)

Matthias Kohl [email protected]

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```curve(log, from = -3, to = 5) curve(glog, from = -3, to = 5, add = TRUE, col = "orange") legend("topleft", fill = c("black", "orange"), legend = c("log", "glog")) curve(log10(x), from = -3, to = 5) curve(glog10(x), from = -3, to = 5, add = TRUE, col = "orange") legend("topleft", fill = c("black", "orange"), legend = c("log10", "glog10")) inv.glog(glog(10)) inv.glog(glog(10, base = 3), base = 3) inv.glog10(glog10(10)) inv.glog2(glog2(10)) ```

stamats/MKmisc documentation built on Dec. 14, 2018, 6:54 a.m.