10 August 2013 8:27:54.127 PM JACOBI_POLYNOMIAL_PRB FORTRAN77 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 0.00 1.00 0.50 1.000000000000000 1.000000000000000 0.0 1 0.00 1.00 0.50 0.2500000000000000 0.2500000000000000 0.0 2 0.00 1.00 0.50 -0.3750000000000000 -0.3750000000000000 0.0 3 0.00 1.00 0.50 -0.4843750000000000 -0.4843750000000000 0.0 4 0.00 1.00 0.50 -0.1328125000000000 -0.1328125000000000 0.0 5 0.00 1.00 0.50 0.2753906250000000 0.2753906250000000 0.0 5 1.00 1.00 0.50 -0.1640625000000000 -0.1640625000000000 0.0 5 2.00 1.00 0.50 -1.174804687500000 -1.174804687500000 0.0 5 3.00 1.00 0.50 -2.361328125000000 -2.361328125000000 0.0 5 4.00 1.00 0.50 -2.616210937500000 -2.616210937500000 0.0 5 5.00 1.00 0.50 0.1171875000000000 0.1171875000000000 0.0 5 0.00 2.00 0.50 0.4218750000000000 0.4218750000000000 0.0 5 0.00 3.00 0.50 0.5048828125000000 0.5048828125000000 0.0 5 0.00 4.00 0.50 0.5097656250000000 0.5097656250000000 0.0 5 0.00 5.00 0.50 0.4306640625000000 0.4306640625000000 0.0 5 0.00 1.00 -1.00 -6.000000000000000 -6.000000000000000 0.0 5 0.00 1.00 -0.80 0.3862000000000000E-01 0.3861999999999950E-01 0.51E-15 5 0.00 1.00 -0.60 0.8118400000000000 0.8118400000000000 0.0 5 0.00 1.00 -0.40 0.3666000000000000E-01 0.3666000000000022E-01 -.22E-15 5 0.00 1.00 -0.20 -0.4851200000000000 -0.4851200000000001 0.56E-16 5 0.00 1.00 0.00 -0.3125000000000000 -0.3125000000000000 0.0 5 0.00 1.00 0.20 0.1891200000000000 0.1891200000000000 -.28E-16 5 0.00 1.00 0.40 0.4023400000000000 0.4023400000000000 0.0 5 0.00 1.00 0.60 0.1216000000000000E-01 0.1216000000000003E-01 -.28E-16 5 0.00 1.00 0.80 -0.4396200000000000 -0.4396200000000000 -.56E-16 5 0.00 1.00 1.00 1.000000000000000 1.000000000000000 0.0 TEST02: J_POLYNOMIAL_ZEROS computes the zeros of J(n,a,b,x); Check by calling J_POLYNOMIAL there. Zeros for J(1,0.5,0.5) 1: 0.0000000 Evaluate J(1,0.5,0.5) 1: 0.0000000 Zeros for J(2,0.5,0.5) 1: -0.50000000 2: 0.50000000 Evaluate J(2,0.5,0.5) 1: -0.29605947E-15 2: -0.29605947E-15 Zeros for J(3,0.5,0.5) 1: -0.70710678 2: 0.65919492E-16 3: 0.70710678 Evaluate J(3,0.5,0.5) 1: 0.35527137E-15 2: -0.14419889E-15 3: -0.82896653E-15 Zeros for J(4,0.5,0.5) 1: -0.80901699 2: -0.30901699 3: 0.30901699 4: 0.80901699 Evaluate J(4,0.5,0.5) 1: 0.40602442E-15 2: 0.20301221E-15 3: 0.55828358E-15 4: 0.14210855E-14 Zeros for J(5,0.5,0.5) 1: -0.86602540 2: -0.50000000 3: 0.59524903E-16 4: 0.50000000 5: 0.86602540 Evaluate J(5,0.5,0.5) 1: -0.30527021E-14 2: -0.57896075E-15 3: 0.16113577E-15 4: 0.57896075E-15 5: 0.23158430E-14 Zeros for J(1,1.0,1.5) 1: 0.11111111 Evaluate J(1,1.0,1.5) 1: 0.0000000 Zeros for J(2,1.0,1.5) 1: -0.34821494 2: 0.50206110 Evaluate J(2,1.0,1.5) 1: -0.17544265E-15 2: -0.35088530E-15 Zeros for J(3,1.0,1.5) 1: -0.57848568 2: 0.70894307E-01 3: 0.68406196 Evaluate J(3,1.0,1.5) 1: 0.10600171E-14 2: -0.99376606E-16 3: -0.66251071E-15 Zeros for J(4,1.0,1.5) 1: -0.70679273 2: -0.21741688 3: 0.33231443 4: 0.78237136 Evaluate J(4,1.0,1.5) 1: 0.0000000 2: -0.12860502E-15 3: -0.25721004E-15 4: -0.12860502E-14 Zeros for J(5,1.0,1.5) 1: -0.78483704 2: -0.40911051 3: 0.52073582E-01 4: 0.50066852 5: 0.84120545 Evaluate J(5,1.0,1.5) 1: -0.28872848E-15 2: -0.11549139E-14 3: 0.81204884E-16 4: 0.72182119E-16 5: -0.18767351E-14 Zeros for J(1,2.0,0.5) 1: -0.33333333 Evaluate J(1,2.0,0.5) 1: 0.0000000 Zeros for J(2,2.0,0.5) 1: -0.64566145 2: 0.18412299 Evaluate J(2,2.0,0.5) 1: -0.35088530E-15 2: -0.87721325E-16 Zeros for J(3,2.0,0.5) 1: -0.78004368 2: -0.21279334 3: 0.46342525 Evaluate J(3,2.0,0.5) 1: -0.39750643E-15 2: 0.16562768E-15 3: 0.18550300E-14 Zeros for J(4,2.0,0.5) 1: -0.85018574 2: -0.44433606 3: 0.99506941E-01 4: 0.62358629 Evaluate J(4,2.0,0.5) 1: 0.77163012E-15 2: 0.12860502E-15 3: -0.45011757E-15 4: 0.77163012E-15 Zeros for J(5,2.0,0.5) 1: -0.89140382 2: -0.58871047 3: -0.15628511 4: 0.31397034 5: 0.72242906 Evaluate J(5,2.0,0.5) 1: -0.14436424E-14 2: 0.57745695E-15 3: 0.46918377E-15 4: -0.50527483E-15 5: 0.57745695E-15 TEST03: J_QUADRATURE_RULE computes the quadrature rule associated with J(n,a,b,x); X W 1: -0.810587 0.620279E-02 2: -0.550876 0.619382E-01 3: -0.230689 0.216462 4: 0.113888 0.398821 5: 0.443600 0.431011 6: 0.720815 0.259969 7: 0.913850 0.622568E-01 Use the quadrature rule to estimate: Q = Integral (-1