/* laphi.h  Lagrange Phi functions, orthogonal polynomials    */
/*         function prototype naming convention:              */
/*           phi            basic Lagrange polynomial         */
/*           phip           first derivative "p for prime"    */
/*           phipp          second derivative,  etc           */
/*                                                            */
/* example  phip(x, i, n, xg[]) is                            */
/*                     ^__ nth degree                         */
/*                  ^__ ith polynomial in set                 */
/*             ^___first derivative "prime"                   */
/*  xg[] is x  grid values, not necessarily uniformly spaced. */
/*  xg[0] is minimum, left boundary.                          */
/*  xg[n] is maximum, right boundary.                         */
/*  All grid coordinates must be in increasing order.         */

/* phi */
double phi(double x, int i, int n, double xg[]);

/* first derivative */
double phip(double x, int i, int n, double xg[]);

/* second derivative */
double phipp(double x, int i, int n, double xg[]);

/* third derivative */
double phippp(double x, int i, int n, double xg[]);

/* fourth derivative */
double phipppp(double x, int i, int n, double xg[]);


/* end laphi.h */