function [ n_data, n, x, fx ] = p01_polynomial_values ( n_data )

%*****************************************************************************80
%
%% p01_polynomial_values(): values of shifted Legendre polynomials.
%
%  Discussion:
%
%    If we denote the Legendre polynomial by P(n)(x), and the shifted 
%    Legendre polynomial by P01(n)(x), then
%
%      P01(n)(x) = P(n)(2*x+1)
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    14 March 2016
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer N_DATA.  The user sets N_DATA to 0 before the first call.  
%
%  Output:
%
%    integer N_DATA.  On each call, the routine increments N_DATA by 1, and
%    returns the corresponding data; when there is no more data, the
%    output value of N_DATA will be 0 again.
%
%    integer N, the order of the function.
%
%    real X, the point where the function is evaluated.
%
%    real FX, the value of the function.
%
  n_max = 22;

  fx_vec = [ ...
      0.1000000000000000E+01, ...
      0.2500000000000000E+00, ...
     -0.4062500000000000E+00, ...
     -0.3359375000000000E+00, ...
      0.1577148437500000E+00, ...
      0.3397216796875000E+00, ...
      0.2427673339843750E-01, ...
     -0.2799186706542969E+00, ...
     -0.1524540185928345E+00, ...
      0.1768244206905365E+00, ...
      0.2212002165615559E+00, ...
      0.0000000000000000E+00, ...
     -0.1475000000000000E+00, ...
     -0.2800000000000000E+00, ...
     -0.3825000000000000E+00, ...
     -0.4400000000000000E+00, ...
     -0.4375000000000000E+00, ...
     -0.3600000000000000E+00, ...
     -0.1925000000000000E+00, ...
      0.8000000000000000E-01, ...
      0.4725000000000000E+00, ...
      0.1000000000000000E+01 ];

  n_vec = [ ...
     0,  1,  2, ...
     3,  4,  5, ...
     6,  7,  8, ...
     9, 10,  3, ...
     3,  3,  3, ...
     3,  3,  3, ...
     3,  3,  3, ...
     3 ];

  x_vec = [ ...
     0.625E+00, ...
     0.625E+00, ...
     0.625E+00, ...
     0.625E+00, ...
     0.625E+00, ...
     0.625E+00, ...
     0.625E+00, ...
     0.625E+00, ...
     0.625E+00, ...
     0.625E+00, ...
     0.625E+00, ...
     0.50E+00, ...
     0.55E+00, ...
     0.60E+00, ...
     0.65E+00, ...
     0.70E+00, ...
     0.75E+00, ...
     0.80E+00, ...
     0.85E+00, ...
     0.90E+00, ...
     0.95E+00, ...
     1.00E+00 ];

  if ( n_data < 0 )
    n_data = 0;
  end

  n_data = n_data + 1;

  if ( n_max < n_data )
    n_data = 0;
    n = 0;
    x = 0.0;
    fx = 0.0;
  else
    n = n_vec(n_data);
    x = x_vec(n_data);
    fx = fx_vec(n_data);
  end

  return
end
