Inverse hyperbolic sine transformation

ihs.R

#' Inverse hyperbolic sine transformation
#' 
#' @param x a numeric vector
#' 
#' @details A useful transformation for skewed data that includes 0's and 
#' negative values

ihs <- function(x) {
    transformed <- log(x + sqrt(x ^ x + 1))
    return(transformed)
}

Correct me if I am wrong but the inverse hyperbolic sine function is x^2 not x^x
Therefore in my mind the code should be like this:

ihs <- function(x) { transformed <- log(x + sqrt(x^2+1)); return(transformed) }