Represents a Chebyshev polynomial series.
SystemObject Extreme.Mathematics.CurvesCurve Extreme.Mathematics.CurvesLinearCombination Extreme.Mathematics.CurvesPolynomialBase Extreme.Mathematics.CurvesChebyshevSeries
Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.1
public sealed class ChebyshevSeries : PolynomialBase
Public NotInheritable Class ChebyshevSeries
public ref class ChebyshevSeries sealed : public PolynomialBase
type ChebyshevSeries =
The ChebyshevSeries type exposes the following members.
Gets the function basis for the polynomial.
Gets or sets the coefficient of the function with the specified
(Inherited from LinearCombination.)
Gets the degree of the polynomial.
(Inherited from PolynomialBase.)
Gets or sets the lower bound of the interval over which this ChebyshevSeries is defined.
|Parameters| (Inherited from Curve.)
Gets the collection of parameters that determine the shape of this
Gets or sets the upper bound of the interval over which this ChebyshevSeries is defined.
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
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
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.