Table 7 The approximation error of \(S_{n_{1},n_{2}}^{q_{1,n_{1}},q_{2,n_{2}}} ( h_{1} ) \) to \(h_{1}\) by means of the partial modulus of continuities
n = 1 × 105 | n = 1 × 104 | n = 1 × 103 | |
|---|---|---|---|
\(\delta _{1}\) | 0.1399192151 × 10−3 | 0.1399247294 × 10−2 | 0.1399798779 × 10−1 |
\(\delta _{2}\) | 0.4764089543 × 10−3 | 0.4765315029 × 10−2 | 0.4777602239 × 10−1 |
\(\omega _{1} ( h_{1};\delta _{1} ) \) | 0.3787201321 × 10−4 | 0.3787350577 × 10−3 | 0.3788843285 × 10−2 |
\(\omega _{2} ( h_{1};\delta _{2} ) \) | 0.1934252196 × 10−3 | 0.1934738320 × 10−2 | 0.1939013872 × 10−1 |
\(E_{7} ( S_{n_{1},n_{2}}^{q_{1,n_{1}},q_{2,n_{2}}} ( h_{1} ) ,h_{1} ) \) | 0.4625944656 × 10−3 | 0.4626946755 × 10−2 | 0.4635796401 × 10−1 |