package org.spaceroots.mantissa.algebra;

/**
 * This class implements Hermite polynomials.

 * 
Hermite polynomials can be defined by the following recurrence
 * relations:
 * 
 *  H0(X)   = 1
 *  H1(X)   = 2X
 *  Hk+1(X) = 2X Hk(X) - 2k Hk-1(X)
 * 


 * @version $Id: Hermite.java 1709 2006-12-03 21:16:50Z luc $
 * @author L. Maisonobe

 */
public class Hermite
  extends OrthogonalPolynomial {

  /** Generator for the Hermite polynomials. */
  private static final CoefficientsGenerator generator =
    new CoefficientsGenerator(new RationalNumber(1l),
                              new RationalNumber(0l),
                              new RationalNumber(2l)) {
    public void setRecurrenceCoefficients(int k) {
      // the recurrence relation is
      // Hk+1(X) = 2X Hk(X) - 2k Hk-1(X)
      setRecurrenceCoefficients(new RationalNumber(0l),
                                new RationalNumber(2l),
                                new RationalNumber(k * 2l));
    }
  };

  /** Simple constructor.
   * Build a degree 0 Hermite polynomial
   */
  public Hermite() {
    super(0, generator);
  }

  /** Simple constructor.
   * Build a degree d Hermite polynomial
   * @param degree degree of the polynomial
   */
  public Hermite(int degree) {
    super(degree, generator);
  }

  private static final long serialVersionUID = 7910082423686662133L;

}