HankelFunction.h File Reference

#include <Rtypes.h>

Go to the source code of this file.

Functions
double	HankelK0 (double x)
double	HankelK1 (double x)
double	HankelKn (int n, double x)

Function Documentation

double HankelK0

(

double

x

)

Definition at line 147 of file HankelFunction.cc.

References BesselI0(), SiStripMonitorClusterAlca_cfi::k0, k0Coefficient, p1, p2, p3, p4, q1, q2, x, and detailsBasic3DVector::y.

Referenced by HankelKn().

                          { 
  const double p1 = k0Coefficient[0][0];
  const double p2 = k0Coefficient[1][0];
  const double p3 = k0Coefficient[2][0];
  const double p4 = k0Coefficient[3][0];
  const double p5 = k0Coefficient[4][0];
  const double p6 = k0Coefficient[5][0];
  const double p7 = k0Coefficient[6][0];

  const double q1 = k0Coefficient[0][1];
  const double q2 = k0Coefficient[1][1];
  const double q3 = k0Coefficient[2][1];
  const double q4 = k0Coefficient[3][1];
  const double q5 = k0Coefficient[4][1];
  const double q6 = k0Coefficient[5][1];
  const double q7 = k0Coefficient[6][1];

  double k0 = 0.;
  if(x <= 2.0) {
    double y = x * x / 4.0;
    k0 = (-TMath::Log(x/2.0)*BesselI0(x)) + (p1 + y*(p2 + y*(p3 + y*(p4 + y*(p5 + y*(p6 + y*p7))))));
  } 
  else {
    double y = (2.0 / x);
    k0 = (TMath::Exp(-x)/TMath::Sqrt(x))*(q1 + y*(q2 + y*(q3 + y*(q4 + y*(q5 + y*(q6 + y*q7))))));
  }

  return k0;
}

double HankelK1

(

double

x

)

Definition at line 177 of file HankelFunction.cc.

References BesselI1(), k1Coefficient, p1, p2, p3, p4, q1, q2, x, and detailsBasic3DVector::y.

Referenced by HankelKn(), and GrandCanonical::ParticleEnergyDensity().

                          { 
  //  (C) Copr. 1986-92 Numerical Recipes Software +7.
  // compute modified Hankel function of the first order
  const double p1 = k1Coefficient[0][0];
  const double p2 = k1Coefficient[1][0];
  const double p3 = k1Coefficient[2][0];
  const double p4 = k1Coefficient[3][0];
  const double p5 = k1Coefficient[4][0];
  const double p6 = k1Coefficient[5][0];
  const double p7 = k1Coefficient[6][0];

  const double q1 = k1Coefficient[0][1];
  const double q2 = k1Coefficient[1][1];
  const double q3 = k1Coefficient[2][1];
  const double q4 = k1Coefficient[3][1];
  const double q5 = k1Coefficient[4][1];
  const double q6 = k1Coefficient[5][1];
  const double q7 = k1Coefficient[6][1];

  double k1 = 0.;

  if(x <= 2.0) { 
    double y = x * x / 4.0;
    k1 = (TMath::Log(x/2.0)*BesselI1(x)) + (1.0/x)*(p1 + y*(p2 + y*(p3 + y*(p4 + y*(p5 + y*(p6 + y*p7))))));
  } 
  else {
    double y = 2.0 / x;
    k1 = (TMath::Exp(-x)/TMath::Sqrt(x))*(q1 + y*(q2 + y*(q3 + y*(q4 + y*(q5 + y*(q6 + y*q7))))));
  }

  return k1;
}

double HankelKn	(	int	n,
		double	x
	)

Definition at line 210 of file HankelFunction.cc.

References trackerHits::c, HankelK0(), HankelK1(), gen::k, kp, and x.

Referenced by GrandCanonical::ParticleEnergyDensity(), NAStrangeDensity::ParticleNumberDensity(), and GrandCanonical::ParticleNumberDensity().

                                 {
  //  (C) Copr. 1986-92 Numerical Recipes Software +7.
  // compute modified Hankel function of the first order
  if(n < 2) throw "Bad argument n in Kn";

  double tox = 2.0 / x;
  double km = HankelK0(x);
  double k = HankelK1(x);
  double kp = 0.;
  
  for(int c = 1; c <= n-1; ++c) {
    kp = km + c * tox * k;
    km = k;
    k = kp;
  }

  return k;
}