Nothing
ghermite.h.inner.products <- function( n, mu )
{
###
### This function returns a vector with n+1 elements
### containing the inner product of an order k generalized Hermite polynomial, Hk(mu,x),
### with itself (i.e. the norm squared) for orders k=0,1,...,n
###
### Parameter
### n = integer highest polynomial order
### mu = first parameter
###
if ( n < 0 )
stop( "negative highest polynomial order" )
if ( n != round( n ) )
stop( "highest polynomial order is not integer" )
if ( mu <= -0.5 )
stop( "mu less than or equal to -0.5" )
if ( abs( mu ) < 1e-6 )
return( hermite.h.inner.products( n ) )
inner.products <- rep( 1, n + 1 )
sqrt.pi <- sqrt( pi )
log.2 <- log( 2 )
mu.plus <- mu + 0.5
j <- 1
for ( k in 0:n ) {
floor.k <- floor( k / 2 )
floor.kp1 <- floor( ( k + 1 ) / 2 )
log.inner.product <- (2 * k ) * log.2 + lgamma( floor.k + 1 ) + lgamma( floor.kp1 + mu.plus )
inner.products[j] <- exp( log.inner.product )
j <- j + 1
}
return ( inner.products )
}
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