From: Asymptotic expansions of the error for hyper-singular integrals with an interval variable
ex ∖ e ∖ n | \(\boldsymbol{2^{3}}\) | \(\boldsymbol{2^{4}}\) | \(\boldsymbol{2^{5}}\) | \(\boldsymbol{2^{6}}\) | \(\boldsymbol{2^{7}}\) | \(\boldsymbol{2^{8}}\) |
---|---|---|---|---|---|---|
\(h^{0}-ex\) | 2.331e − 2 | 6.077e − 3 | 1.573e − 3 | 3.854e − 4 | 9.643e − 5 | 2.411e − 5 |
\(r_{n}^{(0)}\) | 21.9395 | 21.9833 | 21.9957 | 21.9989 | 21.9997 | |
\(h^{2}-ex\) | 3.329e − 4 | 2.363e − 5 | 1.533e − 6 | 9.696e − 8 | 6.065e − 9 | |
\(r_{n}^{(1)}\) | 23.8163 | 23.9463 | 23.9859 | 23.9964 | ||
\(h^{4}-ex\) | 3.014e − 6 | 5.972e − 8 | 1.004e − 9 | 1.597e − 11 | ||
\(r_{n}^{(2)}\) | 25.6571 | 25.8942 | 25.9745 | |||
\(h^{6}-ex\) | 1.284e − 8 | 7.213e − 11 | 2.800e − 13 |