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

%*****************************************************************************80
%
%% CHEBY_T_POLY_VALUES returns values of Chebyshev polynomials T(n,x).
%
%  Discussion:
%
%    In Mathematica, the function can be evaluated by:
%
%      ChebyshevT[n,x]
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    10 July 2015
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Milton Abramowitz and Irene Stegun,
%    Handbook of Mathematical Functions,
%    US Department of Commerce, 1964.
%
%    Stephen Wolfram,
%    The Mathematica Book,
%    Fourth Edition,
%    Wolfram Media / Cambridge University Press, 1999.
%
%  Parameters:
%
%    Input/output, integer N_DATA.  The user sets N_DATA to 0 before the
%    first call.  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.
%
%    Output, integer N, the order of the function.
%
%    Output, real X, the point where the function is evaluated.
%
%    Output, real FX, the value of the function.
%
  n_max = 14;

  fx_vec = [ ...
      0.0000000000000000E+00, ...
      0.1000000000000000E+01, ... 
      0.8000000000000000E+00, ... 
      0.2800000000000000E+00, ... 
     -0.3520000000000000E+00, ... 
     -0.8432000000000000E+00, ... 
     -0.9971200000000000E+00, ... 
     -0.7521920000000000E+00, ... 
     -0.2063872000000000E+00, ... 
      0.4219724800000000E+00, ... 
      0.8815431680000000E+00, ... 
      0.9884965888000000E+00, ... 
      0.7000513740800000E+00, ... 
      0.1315856097280000E+00 ];

  n_vec = [ ...
    -1, ...
     0,  1,  2, ...
     3,  4,  5, ...
     6,  7,  8, ...
     9, 10, 11, ...
    12 ];

  x_vec = [ ...
     0.8E+00, ...
     0.8E+00, ... 
     0.8E+00, ...
     0.8E+00, ...
     0.8E+00, ...
     0.8E+00, ...
     0.8E+00, ...
     0.8E+00, ...
     0.8E+00, ...
     0.8E+00, ...
     0.8E+00, ...
     0.8E+00, ...
     0.8E+00, ...
     0.8E+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
