Class PolynomialsUtils
java.lang.Object
org.apache.commons.math.analysis.polynomials.PolynomialsUtils
A collection of static methods that operate on or return polynomials.
- Since:
- 2.0
- Version:
- $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $
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Method Summary
Modifier and TypeMethodDescriptionstatic PolynomialFunction
createChebyshevPolynomial
(int degree) Create a Chebyshev polynomial of the first kind.static PolynomialFunction
createHermitePolynomial
(int degree) Create a Hermite polynomial.static PolynomialFunction
createLaguerrePolynomial
(int degree) Create a Laguerre polynomial.static PolynomialFunction
createLegendrePolynomial
(int degree) Create a Legendre polynomial.
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Method Details
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createChebyshevPolynomial
Create a Chebyshev polynomial of the first kind.Chebyshev polynomials of the first kind are orthogonal polynomials. They can be defined by the following recurrence relations:
T0(X) = 1 T1(X) = X Tk+1(X) = 2X Tk(X) - Tk-1(X)
- Parameters:
degree
- degree of the polynomial- Returns:
- Chebyshev polynomial of specified degree
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createHermitePolynomial
Create a Hermite polynomial.Hermite polynomials are orthogonal polynomials. They can be defined by the following recurrence relations:
H0(X) = 1 H1(X) = 2X Hk+1(X) = 2X Hk(X) - 2k Hk-1(X)
- Parameters:
degree
- degree of the polynomial- Returns:
- Hermite polynomial of specified degree
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createLaguerrePolynomial
Create a Laguerre polynomial.Laguerre polynomials are orthogonal polynomials. They can be defined by the following recurrence relations:
L0(X) = 1 L1(X) = 1 - X (k+1) Lk+1(X) = (2k + 1 - X) Lk(X) - k Lk-1(X)
- Parameters:
degree
- degree of the polynomial- Returns:
- Laguerre polynomial of specified degree
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createLegendrePolynomial
Create a Legendre polynomial.Legendre polynomials are orthogonal polynomials. They can be defined by the following recurrence relations:
P0(X) = 1 P1(X) = X (k+1) Pk+1(X) = (2k+1) X Pk(X) - k Pk-1(X)
- Parameters:
degree
- degree of the polynomial- Returns:
- Legendre polynomial of specified degree
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