R/Bessel.R

In HypergeoMat: Hypergeometric Function of a Matrix Argument

#' Type one Bessel function of Herz
#'
#' @description Evaluates the type one Bessel function of Herz.
#'
#' @param m truncation weight of the summation, a positive integer
#' @param nu the order parameter, real or complex number with \code{Re(nu)>-1}
#' @param x either a real or complex square matrix,
#'   or a numeric or complex vector, the eigenvalues of the matrix
#'
#' @return A real or complex number.
#' @export
#'
#' @note This function is usually defined
#'   for a symmetric real matrix or a Hermitian complex matrix.
#'
#' @references A. K. Gupta and D. K. Nagar.
#' \emph{Matrix variate distributions}. Chapman and Hall, 1999.
#'
#' @examples # for a scalar x, the relation with the Bessel J-function:
#' t <- 2
#' nu <- 3
#' besselJ(t, nu)
#' BesselA(m=15, t^2/4, nu) * (t/2)^nu
#' # it also holds for a complex variable:
#' if(require("Bessel")) {
#'   t <- 1 + 2i
#'   Bessel::BesselJ(t, nu)
#'   BesselA(m=15, t^2/4, nu) * (t/2)^nu
#' }
BesselA <- function(m, x, nu){
  stopifnot(
    isPositiveInteger(m),
    isScalar(nu),
    Re(nu) > -1
  )
  if(isSquareMatrix(x)){
    stopifnot(!anyNA(x))
    p <- nrow(x)
  }else if(isNumericOrComplex(x)){
    stopifnot(!anyNA(x))
    p <- length(x)
  }else{
    stop("Invalid `x` argument.")
  }
  .hypergeomPFQ(m, NULL, nu+(p+1)/2, -x, alpha = 2) / mvgamma(nu+(p+1)/2, p)
}