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

%*****************************************************************************80
%
%% CHEBY_U_POLY_VALUES returns values of Chebyshev polynomials U(n,x).
%
%  Discussion:
%
%    In Mathematica, the function can be evaluated by:
%
%      ChebyshevU[n,x]
%
%    The Chebyshev U polynomial is a solution to the differential equation:
%
%    (1-X*X) Y'' - 3 X Y' + N (N+2) Y = 0
%
%  First terms:
%
%    U(0)(X) =   1
%    U(1)(X) =   2 X
%    U(2)(X) =   4 X^2 -   1
%    U(3)(X) =   8 X^3 -   4 X
%    U(4)(X) =  16 X^4 -  12 X^2 +  1
%    U(5)(X) =  32 X^5 -  32 X^3 +  6 X
%    U(6)(X) =  64 X^6 -  80 X^4 + 24 X^2 - 1
%    U(7)(X) = 128 X^7 - 192 X^5 + 80 X^3 - 8X
%
%  Recursion:
%
%    U(0)(X) = 1,
%    U(1)(X) = 2 * X,
%    U(N)(X) = 2 * X * U(N-1)(X) - U(N-2)(X)
%
%  Norm:
%
%    Integral ( -1 <= X <= 1 ) ( 1 - X^2 ) * U(N,X)^2 dX = PI/2
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    15 August 2004
%
%  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 = 13;

  fx_vec = [ ...
      0.1000000000000000E+01, ... 
      0.1600000000000000E+01, ... 
      0.1560000000000000E+01, ... 
      0.8960000000000000E+00, ... 
     -0.1264000000000000E+00, ... 
     -0.1098240000000000E+01, ... 
     -0.1630784000000000E+01, ... 
     -0.1511014400000000E+01, ... 
     -0.7868390400000000E+00, ... 
      0.2520719360000000E+00, ... 
      0.1190154137600000E+01, ... 
      0.1652174684160000E+01, ... 
      0.1453325357056000E+01 ];

  n_vec = [ ...
     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 ];

  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