From: Asymptotic expansions of the error for hyper-singular integrals with an interval variable
ex ∖ e ∖ n | \(\boldsymbol{2^{3}}\) | \(\boldsymbol{2^{4}}\) | \(\boldsymbol{2^{5}}\) | \(\boldsymbol{2^{6}}\) | \(\boldsymbol{2^{7}}\) | \(\boldsymbol{2^{8}}\) | \(\boldsymbol{2^{9}}\) |
---|---|---|---|---|---|---|---|
\(h^{0}-ex\) | 3.600e − 2 | 1.240e − 2 | 4.286e − 3 | 1.490e − 3 | 5.202e − 4 | 1.823e − 4 | 6.405e − 5 |
\(r_{n}^{(0)}\) | 21.5379 | 21.5326 | 21.5246 | 21.5178 | 21.5128 | 21.5091 | |
\(h^{2}-ex\) | 5.107e − 4 | 1.514e − 4 | 3.955e − 5 | 9.998e − 6 | 2.506e − 6 | 6.271e − 7 | |
\(r_{n}^{(1)}\) | 21.7538 | 21.9368 | 21.9840 | 21.9960 | 21.9990 | ||
\(h^{4}-ex\) | 3.168e − 5 | 2.262e − 6 | 1.469e − 7 | 9.272e − 9 | 5.810e − 10 | ||
\(r_{n}^{(2)}\) | 23.8081 | 23.9447 | 23.9855 | 23.9963 |