#include <math.h>
extern double F (double);
void approxc2 (unsigned int n, double *c, double *tmpx, double *tmpy)
{
  double pi, h, ai, hi, ya, yb, ci, t0, t1, x2, t2;
  unsigned int i, k;
  pi = 4.0 * atan (1.0);
  h = pi / (double) (n != 1 ? n - 1 : 1);
  ai = 0.0;
  for (i = 0; i < (n + 1) >> 1; i++) {
    hi = h * ai; ai += 1.0; tmpx[i] = cos (hi);
    }
  for (i = (n + 1) >> 1; i < n; i++)
    tmpx[i] = -tmpx[n - (i + 1)];
  for (i = 0; i < n; i++)
    tmpy[i] = F (tmpx[i]);
  h = 2.0 / (double) (n != 1 ? n - 1 : 1);
  if (n > 0) {
      ya = tmpy[0]; yb = tmpy[n - 1];
      }
    else
      ya = yb = 0.0;
  for (i = 0; i < n; i++) {
    ci = 0.5 * (ya + ((i & (unsigned int) 0x1) == 0 ? yb : -yb));
    t0 = 1.0; t1 = tmpx[i]; x2 = 2.0 * t1;
    for (k = 2; k < n; k++) {
      t2 = t1; t1 = t0; t0 = t1 * x2 - t2;
      ci += t0 * tmpy[k - 1];
      }
    c[i] = ci * h;
    }
  if (n > 0)
    c[0] *= 0.5;
  if (n > 1)
    c[n - 1] *= 0.5;
  return;
  }