R/schebyshev.t.inner.products.R

In orthopolynom: Collection of Functions for Orthogonal and Orthonormal Polynomials

schebyshev.t.inner.products <- function( n )
{
###
### 	This function returns a vector with n+1 elements
###	containing the inner product of an order k shifted Chebyshev polynomial
###	of the first kind, Tstar-k(x), with itself (i.e. the norm squared)
###	for orders k=0,1,...,n
###
###	Parameter
###	n = integer highest polynomial order
###
	if ( n < 0 )
		stop( "negative highest polynomial order" )
	if ( n != round( n ) )
		stop( "highest polynomial order is not integer" )
	inner.products <- rep( 0, n + 1 )
	j <- 1
	for ( k in 0:n) {
		if ( k == 0 ) {
			inner.products[j] <- pi
		}
		else {
			inner.products[j] <- pi / 2
		}
		j <- j + 1
	}
	return( inner.products )
}