R/chebyshev.c.inner.products.R

In orthopolynom: Collection of Functions for Orthogonal and Orthonormal Polynomials

chebyshev.c.inner.products <- function( n )
{
###
### This function returns a vector with n+1 elements
### containing the inner product of an order k Chebyshev polynomial
### of the first kind, Ck(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 <- c( 8 * pi, rep( 4 * pi, n ) )
    return ( inner.products )
}