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## org.apache.commons.math.analysis.polynomials
Class PolynomialsUtils

    java.lang.Object
      org.apache.commons.math.analysis.polynomials.PolynomialsUtils

    public class PolynomialsUtils

extends Object

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 aoÃ»t 2010) $

Method Summary
`static 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.

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Method Detail

### createChebyshevPolynomial

    public static PolynomialFunction createChebyshevPolynomial(int degree)

  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

### createHermitePolynomial

    public static PolynomialFunction createHermitePolynomial(int degree)

  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

### createLaguerrePolynomial

    public static PolynomialFunction createLaguerrePolynomial(int degree)

  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

### createLegendrePolynomial

    public static PolynomialFunction createLegendrePolynomial(int degree)

  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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