R/RG.R

In Carlson: Carlson Elliptic Integrals and Incomplete Elliptic Integrals

#' Carlson elliptic integral RG
#' @description Evaluate the Carlson elliptic integral RG.
#'
#' @param x,y,z real or complex numbers; they can be zero
#' @param minerror bound on the relative error passed to
#'   \code{\link{Carlson_RF}} and \code{\link{Carlson_RD}}
#'
#' @return A complex number, the value of the Carlson elliptic integral
#'   \ifelse{html}{\out{R<sub>G</sub>(x,y,z)}}{\eqn{R_G(x,y,z)}{RG(x,y,z)}}.
#' @export
Carlson_RG <- function(x, y, z, minerror = 1e-15){
  zeros <- sum(c(x, y, z) == 0)
  if(zeros == 3L){
    return(0i)
  }
  if(zeros == 2L){
    nonzero <- which(c(x, y, z) != 0)
    return(sqrt(as.complex(c(x, y, z)[nonzero]))/2)
  }
  if(z == 0){
    return(Carlson_RG(y, z, x, minerror))
  }
  x <- as.complex(x); y <- as.complex(y); z <- as.complex(z)
  (z * Carlson_RF_(x, y, z, minerror) -
     (x-z) * (y-z) * Carlson_RD_(x, y, z, minerror)/3 +
      sqrt(x) * sqrt(y) / sqrt(z)) / 2
}