#include <stdio.h>#include <gsl/gsl_math.h>#include <gsl/gsl_sum.h>#define N 20intmain (void){  double t[N];  double sum_accel, err;  double sum = 0;  int n;    gsl_sum_levin_u_workspace * w     = gsl_sum_levin_u_alloc (N);  const double zeta_2 = M_PI * M_PI / 6.0;    /* terms for zeta(2) = \sum_{n=1}^{\infty} 1/n^2 */  for (n = 0; n < N; n++)    {      double np1 = n + 1.0;      t[n] = 1.0 / (np1 * np1);      sum += t[n];    }    gsl_sum_levin_u_accel (t, N, w, &sum_accel, &err);  printf ("term-by-term sum = % .16f using %d terms\n",           sum, N);  printf ("term-by-term sum = % .16f using %d terms\n",           w->sum_plain, w->terms_used);  printf ("exact value      = % .16f\n", zeta_2);  printf ("accelerated sum  = % .16f using %d terms\n",           sum_accel, w->terms_used);  printf ("estimated error  = % .16f\n", err);  printf ("actual error     = % .16f\n",           sum_accel - zeta_2);  gsl_sum_levin_u_free (w);  return 0;}