chebCoeff.Rd
\name{chebCoeff}
\alias{chebCoeff}
\title{Chebyshev Polynomials}
\description{
Chebyshev Coefficients for Chebyshev polynomials of the first kind.
}
\usage{
chebCoeff(fun, a, b, n)
}
\arguments{
\item{fun}{function to be approximated.}
\item{a, b}{endpoints of the interval.}
\item{n}{an integer \code{>= 0}.}
}
\details{
For a function \code{fun} on on the interval \code{[a, b]} determines the
coefficients of the Chebyshev polynomials up to degree \code{n} that will
approximate the function (in L2 norm).
}
\value{
Vector of coefficients for the Chebyshev polynomials, from low to high
degrees (see the example).
}
\references{
Weisstein, Eric W. ``Chebyshev Polynomial of the First Kind."
From MathWorld --- A Wolfram Web Resource.
\url{http://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html}
}
\author{
HwB <hwborchers@googlemail.com>
}
\note{
See the ``Chebfun Project'' <http://www.maths.ox.ac.uk/chebfun/> by
Nick Trefethen.
}
\seealso{
\code{\link{chebPoly}}, \code{\link{chebApprox}}
}
\examples{
## Chebyshev coefficients for x^2 + 1
n <- 4
f2 <- function(x) x^2 + 1
cC <- chebCoeff(f2, -1, 1, n) # 3.0 0 0.5 0 0
cC[1] <- cC[1]/2 # correcting the absolute Chebyshev term
# i.e. 1.5*T_0 + 0.5*T_2
cP <- chebPoly(n) # summing up the polynomial coefficients
p <- cC \%*\% cP # 0 0 1 0 1
}
\keyword{ math }