ChebyshevBasis Class

Use a ChebyshevBasis object to represent a basis for the polynomials in terms of Chebyshev polynomials over a specified interval. A number of mathematical properties of Chebyshev polynomials - in particular their mutual orthogonality over the interval [-1, 1] - make this basis particularly useful for numerical applications.

Chebyshev polynomials have these special properties only over the interval [-1,1]. However, rescaling is applied transparently to allow a ChebyshevBasis to be defined over any finite interval.

Only in rare cases will it be necessary to construct a ChebyshevBasis, as most functionality is available through the ChebyshevSeries class. The most useful members are the FillValues(Double, DenseVector) and FillDerivatives(Double, DenseVector) methods, which allow for efficient calculation of multiple values or derivatives of the polynomials.

Note: The first function (the constant term) is equal to 0.5 instead of the value of 1 of the Chebyshev polynomial of degree 0. The reason is that Chebyshev series are commonly expressed with the constant term multiplied by 0.5. The ChebyshevSeries class follows this convention.