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