Theory and Modern Applications
Table 2 Numerical results of \(\Gamma _{q}(\sigma +1)\) and Δ for \(q = \frac{1}{5}\), \(\frac{1}{2}\), \(\frac{7}{8}\) in Example 4.2 (Algorithm 1)
n | \(q = \frac{ 1}{ 5}\) | \(q = \frac{ 1}{ 2}\) | \(q = \frac{7}{8}\) | |||
|---|---|---|---|---|---|---|
\(\Gamma _{q}(\sigma +1)\) | Δ | \(\Gamma _{q}(\sigma +1)\) | Δ | \(\Gamma _{q}(\sigma +1)\) | Δ | |
1 | 1.3343 | 1.3128E + 01 | 2.3699 | 7.3912E + 00 | 29.1233 | 6.0147E − 01 |
2 | 1.3238 | 1.3232E + 01 | 2.1221 | 8.2545E + 00 | 18.5831 | 9.4262E − 01 |
3 | 1.3217 | 1.3253E + 01 | 2.0124 | 8.7044E + 00 | 13.3129 | 1.3158E + 00 |
4 | 1.3213 | 1.3257E + 01 | 1.9607 | 8.9339E + 00 | 10.2860 | 1.7030E + 00 |
5 | 1.3212 | 1.3258E + 01 | 1.9356 | 9.0499E + 00 | 8.3794 | 2.0905E + 00 |
6 | 1.3212 | 1.3258E + 01 | 1.9232 | 9.1081E + 00 | 7.0969 | 2.4682E + 00 |
â‹® | â‹® | â‹® | â‹® | â‹® | â‹® | â‹® |
14 | 1.3212 | 1.3258E + 01 | 1.9110 | 9.1663E + 00 | 3.7276 | 4.6992E + 00 |
15 | 1.3212 | 1.3258E + 01 | 1.9110 | 9.1665E + 00 | 3.5932 | 4.8750E + 00 |
16 | 1.3212 | 1.3258E + 01 | 1.9109 | 9.1665E + 00 | 3.4811 | 5.0320E + 00 |
17 | 1.3212 | 1.3258E + 01 | 1.9109 | 9.1665E + 00 | 3.3870 | 5.1717E + 00 |
â‹® | â‹® | â‹® | â‹® | â‹® | â‹® | â‹® |
81 | 1.3212 | 1.3258E + 01 | 1.9109 | 9.1666E + 00 | 2.8191 | 6.2137E + 00 |
82 | 1.3212 | 1.3258E + 01 | 1.9109 | 9.1666E + 00 | \( \underline{2}\underline{.}\underline{8190} \) | 6.2137E + 00 |
83 | 1.3212 | 1.3258E + 01 | 1.9109 | 9.1666E + 00 | 2.8190 | 6.2137E + 00 |
84 | 1.3212 | 1.3258E + 01 | 1.9109 | 9.1666E + 00 | 2.8190 | 6.2138E + 00 |
85 | 1.3212 | 1.3258E + 01 | 1.9109 | 9.1666E + 00 | 2.8190 | 6.2138E + 00 |
86 | 1.3212 | 1.3258E + 01 | 1.9109 | 9.1666E + 00 | 2.8190 | 6.2138E + 00 |
87 | 1.3212 | 1.3258E + 01 | 1.9109 | 9.1666E + 00 | 2.8190 | 6.2138E + 00 |