26 March 2023 6:48:13.981 PM jacobi_exactness(): FORTRAN90 version Investigate the polynomial exactness of a Gauss-Jacobi quadrature rule by integrating weighted monomials up to a given degree over the [-1,+1] interval. JACOBI_EXACTNESS: User input: Quadrature rule X file = "jac_o2_a0.5_b1.5_x.txt". Quadrature rule W file = "jac_o2_a0.5_b1.5_w.txt". Quadrature rule R file = "jac_o2_a0.5_b1.5_r.txt". Maximum degree to check = 5 Exponent of (1-x), ALPHA = 0.500000 Exponent of (1+x), BETA = 1.50000 Spatial dimension = 1 Number of points = 2 The quadrature rule to be tested is a Gauss-Jacobi rule ORDER = 2 ALPHA = 0.500000 BETA = 1.50000 Standard rule: Integral ( -1 <= x <= +1 ) (1-x)^alpha (1+x)^beta f(x) dx is to be approximated by sum ( 1 <= I <= ORDER ) w(i) * f(x(i)). Weights W: w( 1) = 0.6369718619318372 w( 2) = 0.9338244648627008 Abscissas X: x( 1) = -0.2742918851774317 x( 2) = 0.6076252185107651 Region R: r( 1) = -1.000000000000000 r( 2) = 1.000000000000000 A Gauss-Jacobi rule would be able to exactly integrate monomials up to and including degree = 3 Error Degree Exponents 0.0000000000002280 0 0 0.0000000000002282 1 1 0.0000000000002280 2 2 0.0000000000002276 3 3 0.3333333333334851 4 4 0.3777777777779197 5 5 JACOBI_EXACTNESS: Normal end of execution. 26 March 2023 6:48:13.982 PM