Chebyshev polynomial interpolation

#define _USE_MATH_DEFINES
#include <math.h>
#include <stdio.h>
#include <stdlib.h>

static double x(int i, int n);
static double w(int n);
static double lambda_inv(int k);
static double T(int k, double x);
static double f(double x);
static double c(int k, int n);
static double f_interpolation(int n, double x);

static double x(int i, int n) {
  return cos(M_PI_2 / n * (2 * i - 1));
}

static double w(int n) {
  return M_PI / n;
}

static double lambda_inv(int k) {
  return (k == 0) ? M_1_PI : M_2_PI;
}

static double T(int k, double x) {
  return (k == 0) ? 1 : (k == 1) ? x : 2 * x * T(k - 1, x) - T(k - 2, x);
}

static double f(double x) {
  return 1. / (1 + 25 * x * x);
}

static double c(int k, int n) {
  double sum = 0.;
  for (int i = 1; i <= n; ++i) {
    double xi = x(i, n);
    sum += w(n) * T(k, xi) * f(xi);
  }
  return lambda_inv(k) * sum;
}

static double f_interpolation(int n, double x) {
  double sum = 0.;
  for (int k = 0; k < n; ++k) {
    sum += c(k, n) * T(k, x);
  }
  return sum;
}

int main(void) {
  FILE *out;
  char name[BUFSIZ];
  int ns[] = { 5, 9, 17 };
  for (size_t i = 0; i < sizeof(ns) / sizeof(ns[0]); ++i) {
    sprintf(name, "%d.dat", ns[i]);
    out = fopen(name, "w");
    for (int x = -100; x <= 100; ++x) {
      double xi = x / 100.;
      fprintf(out, "%lf %lf\n", xi, f_interpolation(ns[i], xi));
    }
    fclose(out);
  }
}