Thu Sep 13 07:38:57 2018 EXACTNESS_TEST Python version: 3.6.5 Test the EXACTNESS library. CHEBYSHEV1_EXACTNESS_TEST Python version: 3.6.5 Test Gauss-Chebyshev1 rules for the Chebyshev1 integral. Density function rho(x) = 1/sqrt(1-x^2). Region: -1 <= x <= +1. Exactness: 2*N-1. CHEBYSHEV1_EXACTNESS: Quadrature rule for Chebyshev1 integral. Order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 1.0000000000000000 CHEBYSHEV1_EXACTNESS: Quadrature rule for Chebyshev1 integral. Order N = 2 Degree Relative Error 0 0.0000000000000003 1 0.0000000000000002 2 0.0000000000000003 3 0.0000000000000003 4 0.3333333333333331 CHEBYSHEV1_EXACTNESS: Quadrature rule for Chebyshev1 integral. Order N = 3 Degree Relative Error 0 0.0000000000000003 1 0.0000000000000000 2 0.0000000000000006 3 0.0000000000000000 4 0.0000000000000006 5 0.0000000000000000 6 0.0999999999999992 CHEBYSHEV1_EXACTNESS: Quadrature rule for Chebyshev1 integral. Order N = 4 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 0.0000000000000001 7 0.0000000000000000 8 0.0285714285714287 CHEBYSHEV1_EXACTNESS: Quadrature rule for Chebyshev1 integral. Order N = 5 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000001 2 0.0000000000000001 3 0.0000000000000001 4 0.0000000000000002 5 0.0000000000000001 6 0.0000000000000001 7 0.0000000000000000 8 0.0000000000000005 9 0.0000000000000000 10 0.0079365079365081 CHEBSHEV1_EXACTNESS_TEST Normal end of execution. CHEBSHEV1_INTEGRAL_TEST Python version: 3.6.5 CHEBYSHEV1_INTEGRAL returns Chebyshev1 integrals of monomials: M(k) = integral ( -1 <= x <= 1 ) x^k / sqrt ( 1 - x^2 ) dx K M(K) 0 3.14159 1 0 2 1.5708 3 0 4 1.1781 5 0 6 0.981748 7 0 8 0.859029 9 0 10 0.773126 CHEBSHEV1_INTEGRAL_TEST Normal end of execution. CHEBYSHEV2_EXACTNESS_TEST Python version: 3.6.5 Test Gauss-Chebyshev2 rules for the Chebyshev2 integral. Density function rho(x) = sqrt(1-x^2). Region: -1 <= x <= +1. Exactness: 2*N-1. CHEBYSHEV2_EXACTNESS: Quadrature rule for Chebyshev2 integral. Order N = 1 Degree Relative Error 0 0.0000000000000003 1 0.0000000000000000 2 1.0000000000000000 CHEBYSHEV2_EXACTNESS: Quadrature rule for Chebyshev2 integral. Order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000002 2 0.0000000000000000 3 0.0000000000000000 4 0.5000000000000000 CHEBYSHEV2_EXACTNESS: Quadrature rule for Chebyshev2 integral. Order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000002 2 0.0000000000000000 3 0.0000000000000001 4 0.0000000000000000 5 0.0000000000000000 6 0.1999999999999999 CHEBYSHEV2_EXACTNESS: Quadrature rule for Chebyshev2 integral. Order N = 4 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000003 5 0.0000000000000000 6 0.0000000000000001 7 0.0000000000000000 8 0.0714285714285713 CHEBYSHEV2_EXACTNESS: Quadrature rule for Chebyshev2 integral. Order N = 5 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000001 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000001 5 0.0000000000000000 6 0.0000000000000005 7 0.0000000000000000 8 0.0000000000000003 9 0.0000000000000000 10 0.0238095238095231 CHEBSHEV2_EXACTNESS_TEST Normal end of execution. CHEBSHEV2_INTEGRAL_TEST Python version: 3.6.5 CHEBYSHEV2_INTEGRAL returns Chebyshev2 integrals of monomials: M(k) = integral ( -1 <= x <= 1 ) x^k * sqrt ( 1 - x^2 ) dx K M(K) 0 1.5708 1 0 2 0.392699 3 0 4 0.19635 5 0 6 0.122718 7 0 8 0.0859029 9 0 10 0.0644272 CHEBSHEV2_INTEGRAL_TEST Normal end of execution. CHEBYSHEV3_EXACTNESS_TEST Python version: 3.6.5 Test Gauss-Chebyshev3 rules for the Chebyshev1 integral. Density function rho(x) = 1/sqrt(1-x^2). Region: -1 <= x <= +1. Exactness: 2*N-3. CHEBYSHEV1_EXACTNESS: Quadrature rule for Chebyshev1 integral. Order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 1.0000000000000000 CHEBYSHEV1_EXACTNESS: Quadrature rule for Chebyshev1 integral. Order N = 2 Degree Relative Error 0 0.0000000000000003 1 0.0000000000000000 2 1.0000000000000007 CHEBYSHEV1_EXACTNESS: Quadrature rule for Chebyshev1 integral. Order N = 3 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.3333333333333333 CHEBYSHEV1_EXACTNESS: Quadrature rule for Chebyshev1 integral. Order N = 4 Degree Relative Error 0 0.0000000000000003 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 0.1000000000000000 CHEBYSHEV1_EXACTNESS: Quadrature rule for Chebyshev1 integral. Order N = 5 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000001 4 0.0000000000000002 5 0.0000000000000001 6 0.0000000000000000 7 0.0000000000000001 8 0.0285714285714283 CHEBSHEV3_EXACTNESS_TEST Normal end of execution. CLENSHAW_CURTIS_EXACTNESS_TEST Python version: 3.6.5 Test Clenshaw-Curtis rules on Legendre integrals. Density function rho(x) = 1. Region: -1 <= x <= +1. Exactness: N for N odd, N-1 for N even. LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 1.0000000000000000 LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 2.0000000000000004 LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 3 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.6666666666666665 LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 4 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.1666666666666668 LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 5 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.0000000000000001 5 0.0000000000000000 6 0.0666666666666664 CLENSHAW_CURTIS_EXACTNESS_TEST Normal end of execution. FEJER1_EXACTNESS_TEST Python version: 3.6.5 Test Fejer Type 1 rules on Legendre integrals. Density function rho(x) = 1. Region: -1 <= x <= +1. Exactness: N for N odd, N-1 for N even. LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 1.0000000000000000 LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.4999999999999997 LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 3 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.2500000000000002 LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 4 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000001 2 0.0000000000000002 3 0.0000000000000000 4 0.0416666666666664 LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 5 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000001 2 0.0000000000000002 3 0.0000000000000001 4 0.0000000000000003 5 0.0000000000000000 6 0.0208333333333331 FEJER1_EXACTNESS_TEST Normal end of execution. FEJER2_EXACTNESS_TEST; Python version: 3.6.5 Test Fejer Type 2 rules on Legendre integrals. Density function rho(x) = 1. Region: -1 <= x <= +1. Exactness: N for N odd, N-1 for N even. LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 1.0000000000000000 LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.2499999999999999 LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.1666666666666666 LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 4 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.0624999999999999 LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 5 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.0000000000000003 5 0.0000000000000000 6 0.0374999999999997 FEJER2_EXACTNESS_TEST Normal end of execution. GEGENBAUER_EXACTNESS_TEST Python version: 3.6.5 Test Gauss-Gegenbauer rules on Gegenbauer integrals. Density function rho(x) = 1. Using Lambda = 1.75 Region: -1 <= x <= +1. Exactness: 2*N-1. GEGENBAUER_EXACTNESS: Quadrature rule for Gegenbauer integral. Lambda = 1.75 Rule of order N = 1 Degree Relative Error 0 0.0000000000000004 1 0.0000000000000000 2 1.0000000000000000 GEGENBAUER_EXACTNESS: Quadrature rule for Gegenbauer integral. Lambda = 1.75 Rule of order N = 2 Degree Relative Error 0 0.0000000000000005 1 0.0000000000000000 2 0.0000000000000010 3 0.0000000000000000 4 0.5454545454545461 GEGENBAUER_EXACTNESS: Quadrature rule for Gegenbauer integral. Lambda = 1.75 Rule of order N = 3 Degree Relative Error 0 0.0000000000000004 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.0000000000000011 5 0.0000000000000000 6 0.2400000000000013 GEGENBAUER_EXACTNESS: Quadrature rule for Gegenbauer integral. Lambda = 1.75 Rule of order N = 4 Degree Relative Error 0 0.0000000000000004 1 0.0000000000000000 2 0.0000000000000012 3 0.0000000000000001 4 0.0000000000000023 5 0.0000000000000001 6 0.0000000000000028 7 0.0000000000000001 8 0.0938345864661684 GEGENBAUER_EXACTNESS: Quadrature rule for Gegenbauer integral. Lambda = 1.75 Rule of order N = 5 Degree Relative Error 0 0.0000000000000005 1 0.0000000000000002 2 0.0000000000000007 3 0.0000000000000001 4 0.0000000000000006 5 0.0000000000000000 6 0.0000000000000009 7 0.0000000000000000 8 0.0000000000000013 9 0.0000000000000000 10 0.0339980385746992 GEGENBAUER_EXACTNESS_TEST Normal end of execution. GEGENBAUER_INTEGRAL_TEST Python version: 3.6.5 GEGENBAUER_INTEGRAL returns Gegenbauer integrals of monomials: M(k) = integral ( -1 <= x <= 1 ) (1-x^2)^(lambda-1/2) dx Here, we use lambda = 1.75 K M(K) 0 1.2486 1 0 2 0.227018 3 0 4 0.0908072 5 0 6 0.0477933 7 0 8 0.0290915 9 0 10 0.0193944 GEGENBAUER_INTEGRAL_TEST Normal end of execution. HERMITE_1_EXACTNESS_TEST Python version: 3.6.5 Test Gauss-Hermite rules on Hermite integrals. Density function rho(x) = 1. Region: -oo < x < +oo. Exactness: 2N-1. HERMITE_EXACTNESS: Quadrature rule for Hermite integral. Rule of order N = 1 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 1.0000000000000000 HERMITE_EXACTNESS: Quadrature rule for Hermite integral. Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000003 3 0.0000000000000000 4 0.6666666666666666 HERMITE_EXACTNESS: Quadrature rule for Hermite integral. Rule of order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000003 3 0.0000000000000000 4 0.0000000000000005 5 0.0000000000000000 6 0.4000000000000003 HERMITE_EXACTNESS: Quadrature rule for Hermite integral. Rule of order N = 4 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000003 5 0.0000000000000000 6 0.0000000000000004 7 0.0000000000000000 8 0.2285714285714290 HERMITE_EXACTNESS: Quadrature rule for Hermite integral. Rule of order N = 5 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 0.0000000000000000 7 0.0000000000000002 8 0.0000000000000000 9 0.0000000000000006 10 0.1269841269841272 HERMITE_1_EXACTNESS_TEST Normal end of execution. HERMITE_EXACTNESS_TEST Python version: 3.6.5 Test Gauss-Hermite rules on Hermite integrals. Density function rho(x) = exp(-x^2). Region: -oo < x < +oo. Exactness: 2N-1. HERMITE_EXACTNESS: Quadrature rule for Hermite integral. Rule of order N = 1 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 1.0000000000000000 HERMITE_EXACTNESS: Quadrature rule for Hermite integral. Rule of order N = 2 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000004 3 0.0000000000000000 4 0.6666666666666666 HERMITE_EXACTNESS: Quadrature rule for Hermite integral. Rule of order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000003 5 0.0000000000000000 6 0.4000000000000002 HERMITE_EXACTNESS: Quadrature rule for Hermite integral. Rule of order N = 4 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000002 5 0.0000000000000000 6 0.0000000000000003 7 0.0000000000000000 8 0.2285714285714290 HERMITE_EXACTNESS: Quadrature rule for Hermite integral. Rule of order N = 5 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 0.0000000000000000 7 0.0000000000000002 8 0.0000000000000000 9 0.0000000000000006 10 0.1269841269841272 HERMITE_EXACTNESS_TEST Normal end of execution. HERMITE_INTEGRAL_TEST Python version: 3.6.5 HERMITE_INTEGRAL returns Hermite integrals of monomials: M(k) = integral ( -oo <= x <= +oo ) x^k exp(-x^2) dx K M(K) 0 1.77245 1 0 2 0.886227 3 0 4 1.32934 5 0 6 3.32335 7 0 8 11.6317 9 0 10 52.3428 HERMITE_INTEGRAL_TEST Normal end of execution. LAGUERRE_1_EXACTNESS_TEST Python version: 3.6.5 Test quadrature rules on Laguerre integrals. Density function rho(x) = 1. Region: 0 <= x < +oo. Exactness: 2N-1. Quadrature rule for Laguerre integral. Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.5000000000000000 Quadrature rule for Laguerre integral. Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.1666666666666667 Quadrature rule for Laguerre integral. Rule of order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 0.0500000000000000 Quadrature rule for Laguerre integral. Rule of order N = 4 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000001 2 0.0000000000000001 3 0.0000000000000003 4 0.0000000000000001 5 0.0000000000000002 6 0.0000000000000003 7 0.0000000000000002 8 0.0142857142857146 Quadrature rule for Laguerre integral. Rule of order N = 5 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000001 3 0.0000000000000001 4 0.0000000000000001 5 0.0000000000000002 6 0.0000000000000002 7 0.0000000000000002 8 0.0000000000000002 9 0.0000000000000003 10 0.0039682539682542 LAGUERRE_1_EXACTNESS_TEST Normal end of execution. LAGUERRE_EXACTNESS_TEST Python version: 3.6.5 Test Gauss-Laguerre rules on Laguerre integrals. Density function rho(x) = exp(-x). Region: 0 <= x < +oo. Exactness: 2N-1. Quadrature rule for Laguerre integral. Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.5000000000000000 Quadrature rule for Laguerre integral. Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.1666666666666667 Quadrature rule for Laguerre integral. Rule of order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000001 5 0.0000000000000002 6 0.0499999999999998 Quadrature rule for Laguerre integral. Rule of order N = 4 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000001 2 0.0000000000000001 3 0.0000000000000003 4 0.0000000000000001 5 0.0000000000000002 6 0.0000000000000003 7 0.0000000000000002 8 0.0142857142857146 Quadrature rule for Laguerre integral. Rule of order N = 5 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000001 3 0.0000000000000001 4 0.0000000000000001 5 0.0000000000000002 6 0.0000000000000002 7 0.0000000000000004 8 0.0000000000000004 9 0.0000000000000003 10 0.0039682539682542 LAGUERRE_EXACTNESS_TEST Normal end of execution. LAGUERRE_INTEGRAL_TEST Python version: 3.6.5 LAGUERRE_INTEGRAL returns Laguerre integrals of monomials: M(k) = integral ( 0 <= x < +oo ) x^k exp(-x) dx K M(K) 0 1 1 1 2 2 3 6 4 24 5 120 6 720 7 5040 8 40320 9 362880 10 3.6288e+06 LAGUERRE_INTEGRAL_TEST Normal end of execution. LEGENDRE_EXACTNESS_TEST Python version: 3.6.5 Test Gauss-Legendre rules on Legendre integrals. Density function rho(x) = 1. Region: -1 <= x <= +1. Exactness: 2*N-1. LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 1.0000000000000000 LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.4444444444444446 LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.0000000000000001 5 0.0000000000000000 6 0.1599999999999997 LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 4 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 0.0000000000000000 7 0.0000000000000000 8 0.0522448979591837 LEGENDRE_EXACTNESS: Quadrature rule for Legendre integral. Rule of order N = 5 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000001 5 0.0000000000000000 6 0.0000000000000002 7 0.0000000000000000 8 0.0000000000000000 9 0.0000000000000000 10 0.0161249685059211 LEGENDRE_EXACTNESS_TEST Normal end of execution. LEGENDRE_INTEGRAL_TEST Python version: 3.6.5 LEGENDRE_INTEGRAL returns Legendre integrals of monomials: M(k) = integral ( -1 <= x <= 1 ) x^k dx K M(K) 0 2 1 0 2 0.666667 3 0 4 0.4 5 0 6 0.285714 7 0 8 0.222222 9 0 10 0.181818 LEGENDRE_INTEGRAL_TEST Normal end of execution. R8_FACTORIAL_TEST Python version: 3.6.5 R8_FACTORIAL evaluates the factorial function. N Exact Computed 0 1 1 1 1 1 2 2 2 3 6 6 4 24 24 5 120 120 6 720 720 7 5040 5040 8 40320 40320 9 362880 362880 10 3628800 3628800 11 39916800 39916800 12 479001600 479001600 13 6227020800 6227020800 14 87178291200 87178291200 15 1307674368000 1307674368000 16 20922789888000 20922789888000 17 355687428096000 355687428096000 18 6402373705728000 6402373705728000 19 1.21645100408832e+17 1.21645100408832e+17 20 2.43290200817664e+18 2.43290200817664e+18 25 1.551121004333099e+25 1.551121004333099e+25 50 3.041409320171338e+64 3.041409320171338e+64 100 9.332621544394415e+157 9.33262154439441e+157 150 5.713383956445855e+262 5.71338395644585e+262 R8_FACTORIAL_TEST Normal end of execution. R8_FACTORIAL2_TEST Python version: 3.6.5 R8_FACTORIAL2 evaluates the double factorial function. N Exact Computed 0 1 1 1 1 1 2 2 2 3 3 3 4 8 8 5 15 15 6 48 48 7 105 105 8 384 384 9 945 945 10 3840 3840 11 10395 10395 12 46080 46080 13 135135 135135 14 645120 645120 15 2027025 2027025 R8_FACTORIAL2_TEST Normal end of execution. R8_GAMMA_TEST: Python version: 3.6.5 R8_GAMMA evaluates the Gamma function. X GAMMA(X) R8_GAMMA(X) -0.5 -3.544907701811032 -3.544907701811032 -0.01 -100.5871979644108 -100.5871979644108 0.01 99.4325851191506 99.4325851191506 0.1 9.513507698668732 9.513507698668731 0.2 4.590843711998803 4.590843711998803 0.4 2.218159543757688 2.218159543757688 0.5 1.772453850905516 1.772453850905516 0.6 1.489192248812817 1.489192248812817 0.8 1.164229713725303 1.164229713725303 1 1 1 1.1 0.9513507698668732 0.9513507698668732 1.2 0.9181687423997607 0.9181687423997607 1.3 0.8974706963062772 0.8974706963062772 1.4 0.8872638175030753 0.8872638175030754 1.5 0.8862269254527581 0.8862269254527581 1.6 0.8935153492876903 0.8935153492876903 1.7 0.9086387328532904 0.9086387328532904 1.8 0.9313837709802427 0.9313837709802427 1.9 0.9617658319073874 0.9617658319073874 2 1 1 3 2 2 4 6 6 10 362880 362880 20 1.21645100408832e+17 1.216451004088321e+17 30 8.841761993739702e+30 8.841761993739751e+30 R8_GAMMA_TEST Normal end of execution. EXACTNESS_TEST: Normal end of execution. Thu Sep 13 07:38:57 2018