##################################################
################ pearson.beta ####################
##################################################
pearson.beta <- function(m, w) {
   # Function for calculating integral breadth, \beta, of
   # an X-ray reflection using the half-width of FWHM (w)
   # and m parameter from a Pearson fit.
   ## Args: m - shape parameter from Pearson fit (numeric)
   ##       w - half the FWHM for the reflection (numeric)
   ## **** NOTE: gamma(x) out of range for x > 171
   ## Values: The integral breadth of the reflection (numeric)
   # Ref: Birkholz2006, page 96 (Eq. 3.5)
   beta <- ((pi * 2^(2 * (1 - m)) * gamma(2 * m - 1)) /
      ((2^(1 / m) - 1) * (gamma(m))^2)) * w
}