07-Jan-2022 22:40:18 laguerre_product_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test laguerre_product(). LAGUERRE_LINEAR_PRODUCT_TEST Compute a linearly weighted Laguerre product table. Tij = integral ( 0 <= X < +oo ) X^E Li(X) Lj(X) exp(-X) dx where Li(X) = Laguerre polynomial of degree i. Maximum degree P = 5 Exponent E of X = 0 Linearly weighted table: Col: 1 2 3 4 5 Row 1 : 1 1.09376e-15 4.62087e-16 2.56956e-17 -2.44921e-16 2 : 1.09376e-15 1 5.3256e-16 6.7394e-16 5.42968e-16 3 : 4.62087e-16 4.77266e-16 1 6.2797e-16 3.747e-16 4 : 2.56956e-17 6.87818e-16 6.80012e-16 1 2.498e-16 5 :-2.44921e-16 5.42968e-16 3.95517e-16 2.22045e-16 1 6 : -3.1778e-16 1.96024e-16 2.15106e-16 9.71445e-16 -6.66134e-16 Col: 6 Row 1 : -3.1778e-16 2 : 1.68268e-16 3 : 2.15106e-16 4 : 1.02696e-15 5 :-7.21645e-16 6 : 1 LAGUERRE_LINEAR_PRODUCT_TEST Compute a linearly weighted Laguerre product table. Tij = integral ( 0 <= X < +oo ) X^E Li(X) Lj(X) exp(-X) dx where Li(X) = Laguerre polynomial of degree i. Maximum degree P = 5 Exponent E of X = 1 Linearly weighted table: Col: 1 2 3 4 5 Row 1 : 1 -1 4.63198e-16 3.04932e-16 7.48099e-17 2 : -1 3 -2 2.34188e-16 -1.31839e-16 3 : 4.63198e-16 -2 5 -3 6.93889e-16 4 : 3.04932e-16 1.78677e-16 -3 7 -4 5 : 7.48099e-17 -1.8735e-16 6.93889e-16 -4 9 6 :-1.60896e-16 -6.93889e-18 8.32667e-16 -4.44089e-16 -5 Col: 6 Row 1 :-1.60896e-16 2 : 1.04083e-16 3 : 1.11022e-15 4 :-6.66134e-16 5 : -5 6 : 11 LAGUERRE_LINEAR_PRODUCT_TEST Compute a linearly weighted Laguerre product table. Tij = integral ( 0 <= X < +oo ) X^E Li(X) Lj(X) exp(-X) dx where Li(X) = Laguerre polynomial of degree i. Maximum degree P = 5 Exponent E of X = 2 Linearly weighted table: Col: 1 2 3 4 5 Row 1 : 2 -4 2 2.65413e-16 3.67761e-16 2 : -4 14 -16 6 -3.44169e-15 3 : 2 -16 38 -36 12 4 : 2.65413e-16 6 -36 74 -64 5 : 3.67761e-16 -3.44169e-15 12 -64 122 6 :-3.60822e-16 -1.33227e-15 5.32907e-15 20 -100 Col: 6 Row 1 :-3.60822e-16 2 :-2.22045e-16 3 : 4.44089e-15 4 : 20 5 : -100 6 : 182 LAGUERRE_EXPONENTIAL_PRODUCT_TEST Compute an exponentially weighted Laguerre product table. Tij = integral ( 0 <= X < +oo ) exp(B*X) Li(X) Lj(X) exp(-X) dx where Li(X) = Laguerre polynomial of degree i. Maximum degree P = 5 Exponential argument coefficient B = 0.000000 Exponentially weighted table: Col: 1 2 3 4 5 Row 1 : 1 1.15356e-15 1.55678e-15 1.4283e-15 1.18035e-15 2 : 1.15356e-15 1 3.68608e-16 7.36235e-16 7.33854e-16 3 : 1.55678e-15 3.95509e-16 1 -7.63685e-18 1.99425e-16 4 : 1.4283e-15 6.80724e-16 -8.07053e-18 1 3.6646e-17 5 : 1.18035e-15 7.06099e-16 2.0116e-16 -1.88651e-17 1 6 : 7.43028e-16 5.86154e-16 4.47017e-16 1.25767e-17 -3.93782e-16 Col: 6 Row 1 : 7.43028e-16 2 : 6.13042e-16 3 : 4.78242e-16 4 : 6.80879e-17 5 :-4.49293e-16 6 : 1 LAGUERRE_EXPONENTIAL_PRODUCT_TEST Compute an exponentially weighted Laguerre product table. Tij = integral ( 0 <= X < +oo ) exp(B*X) Li(X) Lj(X) exp(-X) dx where Li(X) = Laguerre polynomial of degree i. Maximum degree P = 5 Exponential argument coefficient B = 1.000000 Exponentially weighted table: Col: 1 2 3 4 5 Row 1 : 31.4689 -457.615 4062.42 -24470.3 104929 2 : -457.615 9071.53 -90575.9 578725 -2.56545e+06 3 : 4062.42 -90575.9 965704 -6.41197e+06 2.91007e+07 4 : -24470.3 578725 -6.41197e+06 4.36555e+07 -2.01415e+08 5 : 104929 -2.56545e+06 2.91007e+07 -2.01415e+08 9.39858e+08 6 : -325627 8.11975e+06 -9.34651e+07 6.53856e+08 -3.07441e+09 Col: 6 Row 1 : -325627 2 : 8.11975e+06 3 :-9.34651e+07 4 : 6.53856e+08 5 :-3.07441e+09 6 : 1.01099e+10 laguerre_product_test(): Normal end of execution. 07-Jan-2022 22:40:18