Represents a Chebyshev polynomial series.
SystemObject Extreme.Mathematics.CurvesCurve Extreme.Mathematics.CurvesLinearCombination Extreme.Mathematics.CurvesPolynomialBase Extreme.Mathematics.CurvesChebyshevSeries
Namespace:
Extreme.Mathematics.Curves
Assembly:
Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.1
[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.
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 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.

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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