ChebyshevSeries Class

Chebyshev series is a linear combination of Chebyshev polynomials. The Chebyshev polynomials are never formed explicitly. All calculations can be performed using only the coefficients.

The Chebyshev polynomials provide an alternate basis for representating general polynomials. Two characteristics make Chebyshev polynomials especially attractive. They are mutually orthogonal, and there exists a simple recurrence relation between consecutive polynomials.

Chebyshev polynomials are defined over the interval [-1, 1]. Using Chebyshev expansions outside of this interval is usually not meaningful and is to be avoided. To allow expansions over any finite interval, transformations are applied wherever necessary.

The ChebyshevSeries class inherits from PolynomialBase This class defines a number of properties shared by all polynomial classes. PolynomialBase is itself derived from LinearCombination.

The parameters of a Chebyshev series are the coefficients of the polynomial.

The Degree of a Chebyshev series is the highest degree of a Chebyshev polynomial that appears in the sum. The number of parameters of the series equals the degree plus one.