EllipticIntegrals.h

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#ifndef ELLIPTICINTEGRALS_H
#define ELLIPTICINTEGRALS_H


// ----------------------------------------------------------------------
//
// Bridge object between C++ code and the GSL Elliptic Integral functions
//
// ----------------------------------------------------------------------

#ifndef ZMENVIRONMENT_H
  #include "ZMutility/ZMenvironment.h"
#endif
#include <utility>
#include <vector>
#include <complex>

ZM_BEGIN_NAMESPACE( zmsf )      /*  namespace zmsf  {  */

typedef std::pair<double,double> Dpair;


struct EllipticIntegrals {

// Legendre forms for the elliptic integrals
// =========================================

  static double CompleteK( const double k );

  static Dpair CompleteKErr( const double k ); 

  static double CompleteE( const double k );

  static Dpair CompleteEErr( const double k );

  static double IncompleteF( const double phi, const double k );

  static Dpair IncompleteFErr( const double phi, const double k ); 

  static double IncompleteE( const double phi, const double k );

  static Dpair IncompleteEErr( const double phi, const double k ); 

  static double IncompleteP( const double phi, const double k, double n );

  static Dpair IncompletePErr( const double phi, const double k, double n ); 

  static double IncompleteD( const double phi, const double k, double n );

  static Dpair IncompleteDErr( const double phi, const double k, double n ); 

// Carlson forms for the elliptic integrals
// ========================================

  static double CarlsonRC( const double x, const double y );

  static Dpair CarlsonRCErr( const double x, const double y ); 

  static double CarlsonRD( const double x, const double y, const double z );

  static Dpair CarlsonRDErr( const double x, const double y, const double z ); 

  static double CarlsonRF( const double x, const double y, const double z );

  static Dpair CarlsonRFErr( const double x, const double y, const double z ); 

  static double CarlsonRJ( const double x, const double y,
                    const double z, const double p );

  static Dpair CarlsonRJErr( const double x, const double y,
                      const double z, const double p ); 

};  // EllipticIntegrals

ZM_END_NAMESPACE( zmsf )        /*  }  // namespace zmsf  */

#endif  /* ELLIPTICINTEGRALS_H */

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