Fri May 19 13:32:57 2023 gegenbauer_exactness_test(): Python version: 3.8.10 Test gegenbauer_exactness(). gegenbauer_exactness(): Investigate the polynomial exactness of a Gauss-Gegenbauer quadrature rule by integrating weighted monomials up to a given degree over the [-1,+1] interval. gegenbauer_exactness(): User input: Quadrature rule X file = "gegen_o8_a0.5_x.txt". Quadrature rule W file = "gegen_o8_a0.5_w.txt". gegen_o8_a0.5_w.txt Quadrature rule R file = "gegen_o8_a0.5_r.txt". gegen_o8_a0.5_r.txt Maximum degree to check = 8 Exponent of (1-x^2), ALPHA = 0.5 Number of points = 8 Testing a Gauss-Gegenbauer rule ORDER = 8 ALPHA = 0.5 Standard rule: Integral ( -1 <= x <= +1 ) (1-x^2)^alpha f(x) dx is to be approximated by sum ( 1 <= I <= ORDER ) w(i) * f(x(i)). Weights W: [0.04083295 0.1442256 0.26179939 0.33854023 0.33854023 0.26179939 0.1442256 0.04083295] Abscissas X: [-0.93969262 -0.76604444 -0.5 -0.17364818 0.17364818 0.5 0.76604444 0.93969262] Region R: [-1. 1.] A Gauss-Gegenbauer rule would be able to exactly integrate monomials up to and including degree = 15 Error Degree 0.0000000000000000 0 0.0000000000000006 1 0.0000000000000007 2 0.0000000000000005 3 0.0000000000000007 4 0.0000000000000004 5 0.0000000000000016 6 0.0000000000000004 7 0.0000000000000021 8 gegenbauer_exactness_test(): Normal end of execution. Fri May 19 13:32:57 2023