package signal.lib;

/**
   The gegenbauerPolynomial class calculates the Gegenbauer (Ultraspherical) Polynomial of degree (L,m).
   @see "Orthogonal Polynomials, AMS Colloquium Publications, vol. 23, p. 80."
*/

 public final class gegenbauerPolynomial {
     private static utility SF;
 
 /** Maps [a,b]  to [-1,1].  */   
   public static double tx(double a, double b, double x) {   
     return (2*x-b-a)/(b-a);
   }
     
 /** Three term recurrence relation. */
  public final static double gegenPoly(int k, double LAMDA, double x) { // iterative calc. of Gegenbauer Polys
    double k2,k1,GP=0;

    if (k==0) return 1.0;
    else if (k==1) return 2*LAMDA*x;
    else { // k>1
      k2=1.0;                     // k-2
      k1=2*LAMDA*x;              // k-1
      for (int i=2; i<=k; i++) {
        GP = (1.0/i)*( 2.0*(i+LAMDA-1.0)*x*k1 - (i+2.0*LAMDA-2.0)*k2  );
        k2=k1;
        k1=GP;
      } // i
      return GP;
    } // else
  } // gegenPoly
  
  
 /** Normalization Factor. */
   public final static double h(int m, double L) {  
          return Math.sqrt(Math.PI)*gegenPoly(m,L,1.0)*(SF.gamma(L+0.5)/(SF.gamma(L)*(m+L)));
   } // h
   
 /** Christoffel-Darboux formula. */
   public static double km(int m, double L) { return ( Math.pow(2.0,m)*SF.gamma(L+m))/(SF.fact(m)*SF.gamma(L)); }
  

 } // gegenbauerPolynomial