void qk (int n, const double xgk[], const double wg[], const double wgk[],
	 double fv1[], double fv2[],
	 const gsl_function *f, double a, double b,
	 double * result, double * abserr, 
	 double * resabs, double * resasc);

void qki (int n, const double xgk[], const double wg[], const double wgk[],
	  double fv1[], double fv2[],
	  const gsl_function *f, double a, double b,
	  double * result, double * abserr, 
	  double * resabs, double * resasc);

int
gsl_integration_qag_impl (const gsl_function *f,
			  double a, double b,
			  double epsabs, double epsrel,
			  size_t limit,
			  gsl_integration_workspace * workspace,
			  double * result, double * abserr,
			  gsl_integration_rule * q) ;

void
gsl_integration_qelg (size_t * n, double epstab[], 
		      double * result, double * abserr,
		      double res3la[], size_t * nres) ;

void
gsl_integration_qcheb (gsl_function * f, double a, double b, 
		       double *cheb12, double *cheb24);

int
gsl_integration_qags_impl (const gsl_function *f, 
			   double a, double b, 
			   double epsabs, double epsrel, size_t limit,
			   gsl_integration_workspace * workspace,
			   double * result, double * abserr,
			   gsl_integration_rule * q) ;

int
gsl_integration_qagp_impl (const gsl_function *f,
			   const double *pts, size_t npts,
			   double epsabs, double epsrel, size_t limit,
			   gsl_integration_workspace * workspace,
			   double *result, double *abserr,
			   gsl_integration_rule * q);

void gsl_integration_qcheb (gsl_function * f, double a, double b, 
			    double *cheb12, double *cheb24);