Table 5 The numerical results of QF, EQF, and RR with \(\pmb{t=0.25}\)
From: Asymptotic expansions of the error for hyper-singular integrals with an interval variable
ex ∖ e ∖ n | \(\boldsymbol{2^{3}}\) | \(\boldsymbol{2^{4}}\) | \(\boldsymbol{2^{5}}\) | \(\boldsymbol{2^{6}}\) | \(\boldsymbol{2^{7}}\) | \(\boldsymbol{2^{8}}\) | |
|---|---|---|---|---|---|---|---|
RR | \(h^{0}-ex\) | 3.5318e − 3 | 8.8306e − 4 | 2.2077e − 4 | 5.5193e − 5 | 1.3798e − 5 | |
QF | \(h^{0}-ex\) | 7.8652e − 2 | 2.0782e − 2 | 5.2765e − 3 | 1.3244e − 3 | 3.3144e − 4 | 8.2880e − 5 |
EQF | \(h^{2}-ex\) | 1.4922e − 3 | 1.0794e − 4 | 7.0429e − 6 | 4.4520e − 7 | 2.7905e − 8 | |
\(h^{4}-ex\) | 1.5657e − 5 | 3.1634e − 7 | 5.3531e − 9 | 8.5167e − 11 | |||
\(r_{n}^{(0)}\) | 21.9201 | 21.9777 | 21.9942 | 21.9985 | 21.9996 | ||
\(r_{n}^{(1)}\) | 23.7891 | 23.9379 | 23.9836 | 23.9959 | |||
\(r_{n}^{(2)}\) | 25.6292 | 25.8849 | 25.9740 |