function [ n_data, x, ai ] = airy_ai_values ( n_data ) %% AIRY_AI_VALUES returns some values of the Airy Ai(x) function. % % Discussion: % % The Airy functions Ai(X) and Bi(X) are a pair of linearly independent % solutions of the differential equation: % % W'' - X * W = 0 % % In Mathematica, the function can be evaluated by: % % AiryAi[x] % % Modified: % % 15 September 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, real X, the argument of the function. % % Output, real AI, the value of the Airy AI function. % n_max = 11; ai_vec = [ ... 0.3550280538878172E+00, ... 0.3292031299435381E+00, ... 0.3037031542863820E+00, ... 0.2788064819550049E+00, ... 0.2547423542956763E+00, ... 0.2316936064808335E+00, ... 0.2098000616663795E+00, ... 0.1891624003981501E+00, ... 0.1698463174443649E+00, ... 0.1518868036405444E+00, ... 0.1352924163128814E+00 ]; x_vec = [ ... 0.0E+00, ... 0.1E+00, ... 0.2E+00, ... 0.3E+00, ... 0.4E+00, ... 0.5E+00, ... 0.6E+00, ... 0.7E+00, ... 0.8E+00, ... 0.9E+00, ... 1.0E+00 ]; if ( n_data < 0 ) n_data = 0; end n_data = n_data + 1; if ( n_max < n_data ) n_data = 0; x = 0.0; ai = 0.0; else x = x_vec(n_data); ai = ai_vec(n_data); end