ChebyshevSeries Class

[SerializableAttribute]
public sealed class ChebyshevSeries : PolynomialBase

<SerializableAttribute>
Public NotInheritable Class ChebyshevSeries
	Inherits PolynomialBase

[SerializableAttribute]
public ref class ChebyshevSeries sealed : public PolynomialBase

[<SealedAttribute>]
[<SerializableAttribute>]
type ChebyshevSeries =  
    class
        inherit PolynomialBase
    end

The ChebyshevSeries type exposes the following members.

	Name	Description
	ChebyshevSeries(Int32)	Constructs a new ChebyshevSeries of the specified degree over the interval [-1, 1].
	ChebyshevSeries(VectorDouble)	Constructs a new ChebyshevSeries with the specified coefficients over the interval [-1, 1].
	ChebyshevSeries(Int32, Double, Double)	Constructs a new ChebyshevSeries of the specified degree over the specified interval.
	ChebyshevSeries(VectorDouble, Double, Double)	Constructs a new ChebyshevSeries with the specified coefficients over the specified interval.

	Name	Description
	Basis	Gets the function basis for the polynomial. (Overrides LinearCombinationBasis.)
	Coefficient	Gets or sets the coefficient of the function with the specified index. (Inherited from LinearCombination.)
	Degree	Gets the degree of the polynomial. (Inherited from PolynomialBase.)
	LowerBound	Gets or sets the lower bound of the interval over which this ChebyshevSeries is defined.
	Parameters	Gets the collection of parameters that determine the shape of this Curve. (Inherited from Curve.)
	UpperBound	Gets or sets the upper bound of the interval over which this ChebyshevSeries is defined.

	Name	Description
	Add(LinearCombination)	Adds another LinearCombination to this instance. (Inherited from LinearCombination.)
	Add(Double, LinearCombination)	Adds two Chebyshev series. (Overrides LinearCombinationAdd(Double, LinearCombination).)
	Clone	Constructs an exact copy of this instance. (Inherited from Curve.)
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	FindRoots	Gets the set of X-coordinates where the curve crosses the X-axis. (Inherited from Curve.)
	GetCurveFitter	Returns a CurveFitter object that can be used to fit the curve to data. (Inherited from LinearCombination.)
	GetDerivative	Returns a Curve that represents the derivative of this ChebyshevSeries. (Overrides CurveGetDerivative.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetInterpolatingPolynomial	Calculates the Chebyshev interpolating polynomial of the specified degree over the given interval for the specified function.
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	Integral	Gets the definite integral of the ChebyshevSeries between the specified X-coordinates. (Overrides CurveIntegral(Double, Double).)
	LeastSquaresFit(VectorDouble, VectorDouble, Int32)	Returns the Polynomial that is the best least squares fit through the given set of points.
	LeastSquaresFit(VectorDouble, VectorDouble, Double, Double, Int32)	Returns the Polynomial that is the best least squares fit through the given set of points.
	SetParameter	Sets a curve parameter to the specified value. (Inherited from Curve.)
	SlopeAt	Evaluates the slope or first derivative of a Chebyshev series for a complex number argument. (Overrides LinearCombinationSlopeAt(Double).)
	Solve	Finds the x value where the curve reaches the specified y value. (Inherited from Curve.)
	Subtract(LinearCombination)	Subtracts another LinearCombination from this instance. (Inherited from LinearCombination.)
	TangentAt	Gets the tangent line to the curve at the specified X-coordinate. (Inherited from Curve.)
	ToString	Returns a string that represents the current object. (Inherited from Object.)
	ValueAt	Evaluates the Chebyshev series for a real argument. (Overrides LinearCombinationValueAt(Double).)

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.

Reference