R/hermite.h.polynomials.R

In orthopolynom: Collection of Functions for Orthogonal and Orthonormal Polynomials

hermite.h.polynomials <- function( n, normalized=FALSE )
{
###
###   This function returns a list with n+1 elements
###   containing the order k Hermite polynomials, Hk(x),
###   for orders k=0,1,...,n
###
###   Parameters
###   n = integer highest polynomial order
###   normalized = a boolean value.  if true, the polynomials are normalized
###
   recurrences <- hermite.h.recurrences( n, normalized )
   if ( normalized ) {
       h.0 <- sqrt( pi )
       p.0 <- polynomial( c( 1 / sqrt( h.0 ) ) )
       polynomials <- orthonormal.polynomials( recurrences, p.0 )
   }
   else
       polynomials <- orthogonal.polynomials( recurrences )
   return( polynomials )
   return( NULL )
}