07-Jan-2022 21:58:00 jacobi_polynomial_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test jacobi_polynomial(). jacobi_polynomial_test01(): J_POLYNOMIAL_VALUES stores values of the Jacobi polynomials. J_POLYNOMIAL evaluates the polynomial. Tabulated Computed N A B X J(N,A,B,X) J(N,A,B,X) Error 0 0.000000 1.000000 0.500000 1.0000000000000000e+00 1.0000000000000000e+00 0 1 0.000000 1.000000 0.500000 2.5000000000000000e-01 2.5000000000000000e-01 0 2 0.000000 1.000000 0.500000 -3.7500000000000000e-01 -3.7500000000000000e-01 0 3 0.000000 1.000000 0.500000 -4.8437500000000000e-01 -4.8437500000000000e-01 0 4 0.000000 1.000000 0.500000 -1.3281250000000000e-01 -1.3281250000000000e-01 0 5 0.000000 1.000000 0.500000 2.7539062500000000e-01 2.7539062500000000e-01 0 5 1.000000 1.000000 0.500000 -1.6406250000000000e-01 -1.6406250000000000e-01 0 5 2.000000 1.000000 0.500000 -1.1748046875000000e+00 -1.1748046875000000e+00 0 5 3.000000 1.000000 0.500000 -2.3613281250000000e+00 -2.3613281250000000e+00 0 5 4.000000 1.000000 0.500000 -2.6162109375000000e+00 -2.6162109375000000e+00 0 5 5.000000 1.000000 0.500000 1.1718750000000000e-01 1.1718750000000000e-01 0 5 0.000000 2.000000 0.500000 4.2187500000000000e-01 4.2187500000000000e-01 0 5 0.000000 3.000000 0.500000 5.0488281250000000e-01 5.0488281250000000e-01 0 5 0.000000 4.000000 0.500000 5.0976562500000000e-01 5.0976562500000000e-01 0 5 0.000000 5.000000 0.500000 4.3066406250000000e-01 4.3066406250000000e-01 0 5 0.000000 1.000000 -1.000000 -6.0000000000000000e+00 -6.0000000000000000e+00 0 5 0.000000 1.000000 -0.800000 3.8620000000000002e-02 3.8619999999999495e-02 5.1e-16 5 0.000000 1.000000 -0.600000 8.1184000000000001e-01 8.1184000000000001e-01 0 5 0.000000 1.000000 -0.400000 3.6659999999999998e-02 3.6660000000000220e-02 -2.2e-16 5 0.000000 1.000000 -0.200000 -4.8512000000000000e-01 -4.8512000000000005e-01 5.6e-17 5 0.000000 1.000000 0.000000 -3.1250000000000000e-01 -3.1250000000000000e-01 0 5 0.000000 1.000000 0.200000 1.8912000000000001e-01 1.8912000000000004e-01 -2.8e-17 5 0.000000 1.000000 0.400000 4.0233999999999998e-01 4.0233999999999998e-01 0 5 0.000000 1.000000 0.600000 1.2160000000000001e-02 1.2160000000000028e-02 -2.8e-17 5 0.000000 1.000000 0.800000 -4.3962000000000001e-01 -4.3961999999999996e-01 -5.6e-17 5 0.000000 1.000000 1.000000 1.0000000000000000e+00 1.0000000000000000e+00 0 jacobi_polynomial_test02: J_POLYNOMIAL_ZEROS computes the zeros of J(n,a,b,x); Check by calling J_POLYNOMIAL there. Computed zeros for J(1,0.500000,0.500000,z): 1: 0 Evaluate J(1,0.500000,0.500000,z): 1: 0 Computed zeros for J(2,0.500000,0.500000,z): 1: -0.5 2: 0.5 Evaluate J(2,0.500000,0.500000,z): 1: -2.96059e-16 2: -2.96059e-16 Computed zeros for J(3,0.500000,0.500000,z): 1: -0.707107 2: 6.59195e-17 3: 0.707107 Evaluate J(3,0.500000,0.500000,z): 1: 3.55271e-16 2: -1.44199e-16 3: -8.28967e-16 Computed zeros for J(4,0.500000,0.500000,z): 1: -0.809017 2: -0.309017 3: 0.309017 4: 0.809017 Evaluate J(4,0.500000,0.500000,z): 1: 4.06024e-16 2: 2.03012e-16 3: 5.58284e-16 4: 1.42109e-15 Computed zeros for J(5,0.500000,0.500000,z): 1: -0.866025 2: -0.5 3: 5.95249e-17 4: 0.5 5: 0.866025 Evaluate J(5,0.500000,0.500000,z): 1: -3.0527e-15 2: -5.78961e-16 3: 1.61136e-16 4: 5.78961e-16 5: 2.31584e-15 Computed zeros for J(1,1.000000,1.500000,z): 1: 0.111111 Evaluate J(1,1.000000,1.500000,z): 1: 0 Computed zeros for J(2,1.000000,1.500000,z): 1: -0.348215 2: 0.502061 Evaluate J(2,1.000000,1.500000,z): 1: -1.75443e-16 2: -3.50885e-16 Computed zeros for J(3,1.000000,1.500000,z): 1: -0.578486 2: 0.0708943 3: 0.684062 Evaluate J(3,1.000000,1.500000,z): 1: 1.06002e-15 2: -9.93766e-17 3: -6.62511e-16 Computed zeros for J(4,1.000000,1.500000,z): 1: -0.706793 2: -0.217417 3: 0.332314 4: 0.782371 Evaluate J(4,1.000000,1.500000,z): 1: 0 2: -1.28605e-16 3: -2.5721e-16 4: -1.28605e-15 Computed zeros for J(5,1.000000,1.500000,z): 1: -0.784837 2: -0.409111 3: 0.0520736 4: 0.500669 5: 0.841205 Evaluate J(5,1.000000,1.500000,z): 1: -2.88728e-16 2: -1.15491e-15 3: 8.12049e-17 4: 7.21821e-17 5: -1.87674e-15 Computed zeros for J(1,2.000000,0.500000,z): 1: -0.333333 Evaluate J(1,2.000000,0.500000,z): 1: 0 Computed zeros for J(2,2.000000,0.500000,z): 1: -0.645661 2: 0.184123 Evaluate J(2,2.000000,0.500000,z): 1: -3.50885e-16 2: -8.77213e-17 Computed zeros for J(3,2.000000,0.500000,z): 1: -0.780044 2: -0.212793 3: 0.463425 Evaluate J(3,2.000000,0.500000,z): 1: -3.97506e-16 2: 1.65628e-16 3: 1.85503e-15 Computed zeros for J(4,2.000000,0.500000,z): 1: -0.850186 2: -0.444336 3: 0.0995069 4: 0.623586 Evaluate J(4,2.000000,0.500000,z): 1: 7.7163e-16 2: 1.28605e-16 3: -4.50118e-16 4: 7.7163e-16 Computed zeros for J(5,2.000000,0.500000,z): 1: -0.891404 2: -0.58871 3: -0.156285 4: 0.31397 5: 0.722429 Evaluate J(5,2.000000,0.500000,z): 1: -1.44364e-15 2: 5.77457e-16 3: 4.69184e-16 4: -5.05275e-16 5: 5.77457e-16 jacobi_polynomial_test03(): J_QUADRATURE_RULE computes the quadrature rule associated with J(n,a,b,x); X W 1: -0.810587 0.00620279 2: -0.550876 0.0619382 3: -0.230689 0.216462 4: 0.113888 0.398821 5: 0.4436 0.431011 6: 0.720815 0.259969 7: 0.91385 0.0622568 Use the quadrature rule to estimate: Q = Integral (-1