double biharmonic_exact_r1 ( double X, double Y, double a, double b, double c, 
  double d, double e, double f, double g );
double biharmonic_exact_r2 ( double X, double Y, double a, double b, double c, 
  double d, double e, double f, double g );
double biharmonic_exact_r3 ( double X, double Y, double a, double b, double c, 
  double d, double e, double f );
double biharmonic_exact_w1 ( double X, double Y, double a, double b, double c, 
  double d, double e, double f, double g );
double biharmonic_exact_w2 ( double X, double Y, double a, double b, double c, 
  double d, double e, double f, double g );
double biharmonic_exact_w3 ( double X, double Y, double a, double b, double c, 
  double d, double e, double f );