/* lobatto_shape.h  zero at -1 and 1  page 25 Solin   */
/*                  and kernel functions  page 27     */
/*                  lobatto are integrated Legendre ? */
/*    normalized derivatives of Lobatto are Legendre  */

double L2(double x);
double L3(double x);
double L4(double x);
double L5(double x);
double L6(double x);
double L7(double x);
double L8(double x);

/* kernel functions   -4.0*L_k-2(x)/(x*x-1.0)  */
double ph0(double x);
double ph1(double x);
double ph2(double x);
double ph3(double x);
double ph4(double x);
double ph5(double x);
double ph6(double x);