04 March 2022 02:04:23 PM JACOBI_POLYNOMIAL_TEST C++ version Test the JACOBI_POLYNOMIAL library. 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 1 0.5 1 1 0 1 0 1 0.5 0.25 0.25 0 2 0 1 0.5 -0.375 -0.375 0 3 0 1 0.5 -0.484375 -0.484375 0 4 0 1 0.5 -0.132812 -0.132812 0 5 0 1 0.5 0.275391 0.275391 0 5 1 1 0.5 -0.164062 -0.164062 0 5 2 1 0.5 -1.1748 -1.1748 0 5 3 1 0.5 -2.36133 -2.36133 0 5 4 1 0.5 -2.61621 -2.61621 0 5 5 1 0.5 0.117188 0.117188 0 5 0 2 0.5 0.421875 0.421875 0 5 0 3 0.5 0.504883 0.504883 0 5 0 4 0.5 0.509766 0.509766 0 5 0 5 0.5 0.430664 0.430664 0 5 0 1 -1 -6 -6 0 5 0 1 -0.8 0.03862 0.03862 5.06539e-16 5 0 1 -0.6 0.81184 0.81184 0 5 0 1 -0.4 0.03666 0.03666 -2.22045e-16 5 0 1 -0.2 -0.48512 -0.48512 5.55112e-17 5 0 1 0 -0.3125 -0.3125 0 5 0 1 0.2 0.18912 0.18912 -2.77556e-17 5 0 1 0.4 0.40234 0.40234 0 5 0 1 0.6 0.01216 0.01216 -2.77556e-17 5 0 1 0.8 -0.43962 -0.43962 -5.55112e-17 5 0 1 1 1 1 0 TEST02: J_POLYNOMIAL_ZEROS computes the zeros of J(n,a,b,x); Check by calling J_POLYNOMIAL there. Zeros for J(1,0.500000,0.500000) 0: 0 Evaluate J(1,0.500000,0.500000) 0: 0 Zeros for J(2,0.500000,0.500000) 0: -0.5 1: 0.5 Evaluate J(2,0.500000,0.500000) 0: -2.96059e-16 1: -2.96059e-16 Zeros for J(3,0.500000,0.500000) 0: -0.707107 1: 6.59195e-17 2: 0.707107 Evaluate J(3,0.500000,0.500000) 0: 3.55271e-16 1: -1.44199e-16 2: -8.28967e-16 Zeros for J(4,0.500000,0.500000) 0: -0.809017 1: -0.309017 2: 0.309017 3: 0.809017 Evaluate J(4,0.500000,0.500000) 0: 4.06024e-16 1: 2.03012e-16 2: 5.58284e-16 3: 1.42109e-15 Zeros for J(5,0.500000,0.500000) 0: -0.866025 1: -0.5 2: 5.95249e-17 3: 0.5 4: 0.866025 Evaluate J(5,0.500000,0.500000) 0: -3.0527e-15 1: -5.78961e-16 2: 1.61136e-16 3: 5.78961e-16 4: 2.31584e-15 Zeros for J(1,1.000000,1.500000) 0: 0.111111 Evaluate J(1,1.000000,1.500000) 0: 0 Zeros for J(2,1.000000,1.500000) 0: -0.348215 1: 0.502061 Evaluate J(2,1.000000,1.500000) 0: -1.75443e-16 1: -3.50885e-16 Zeros for J(3,1.000000,1.500000) 0: -0.578486 1: 0.0708943 2: 0.684062 Evaluate J(3,1.000000,1.500000) 0: 1.06002e-15 1: -9.93766e-17 2: -6.62511e-16 Zeros for J(4,1.000000,1.500000) 0: -0.706793 1: -0.217417 2: 0.332314 3: 0.782371 Evaluate J(4,1.000000,1.500000) 0: 0 1: -1.28605e-16 2: -2.5721e-16 3: -1.28605e-15 Zeros for J(5,1.000000,1.500000) 0: -0.784837 1: -0.409111 2: 0.0520736 3: 0.500669 4: 0.841205 Evaluate J(5,1.000000,1.500000) 0: -2.88728e-16 1: -1.15491e-15 2: 8.12049e-17 3: 7.21821e-17 4: -1.87674e-15 Zeros for J(1,2.000000,0.500000) 0: -0.333333 Evaluate J(1,2.000000,0.500000) 0: 0 Zeros for J(2,2.000000,0.500000) 0: -0.645661 1: 0.184123 Evaluate J(2,2.000000,0.500000) 0: -3.50885e-16 1: -8.77213e-17 Zeros for J(3,2.000000,0.500000) 0: -0.780044 1: -0.212793 2: 0.463425 Evaluate J(3,2.000000,0.500000) 0: -3.97506e-16 1: 1.65628e-16 2: 1.85503e-15 Zeros for J(4,2.000000,0.500000) 0: -0.850186 1: -0.444336 2: 0.0995069 3: 0.623586 Evaluate J(4,2.000000,0.500000) 0: 7.7163e-16 1: 1.28605e-16 2: -4.50118e-16 3: 7.7163e-16 Zeros for J(5,2.000000,0.500000) 0: -0.891404 1: -0.58871 2: -0.156285 3: 0.31397 4: 0.722429 Evaluate J(5,2.000000,0.500000) 0: -1.44364e-15 1: 5.77457e-16 2: 4.69184e-16 3: -5.05275e-16 4: 5.77457e-16 TEST03: J_QUADRATURE_RULE computes the quadrature rule associated with J(n,a,b,x); X W 0: -0.810587 0.00620279 1: -0.550876 0.0619382 2: -0.230689 0.216462 3: 0.113888 0.398821 4: 0.4436 0.431011 5: 0.720815 0.259969 6: 0.91385 0.0622568 Use the quadrature rule to estimate: Q = Integral (-1