Table 4 Numerical results of Σ̆ for \(q = \frac{1}{7}\) in Example 5.1
n | \(\Gamma _{q}(\nu +1)\) | \(\Gamma _{q}(\nu -\sigma +1)\) | Σ̆ | \(\omega _{\varphi}\) |
|---|---|---|---|---|
\(q = \frac{1}{7}\) | ||||
1 | 1.14283 | 1.18028 | 0.01818 | 0.89123 |
2 | 1.14027 | 1.18063 | 0.01818 | 0.89323 |
3 | 1.13990 | 1.18068 | 0.01818 | 0.89351 |
4 | 1.13985 | 1.18069 | 0.01818 | 0.89355 |
5 | 1.13984 | 1.18069 | 0.01818 |
|
6 | 1.13984 | 1.18069 | 0.01818 | 0.89356 |
\(q = \frac{1}{2}\) | ||||
1 | 2.10842 | 2.02631 | 0.01054 | 0.47934 |
2 | 1.99300 | 2.03657 | 0.01053 | 0.50710 |
3 | 1.94055 | 2.04137 | 0.01053 | 0.52080 |
4 | 1.91550 | 2.04369 | 0.01052 | 0.52761 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
13 | 1.89123 | 2.04597 | 0.01052 | 0.53438 |
14 | 1.89121 | 2.04597 | 0.01052 |
|
15 | 1.89120 | 2.04597 | 0.01052 | 0.53439 |
\(q = \frac{8}{9}\) | ||||
1 | 21.16106 | 8.65603 | 0.00238 | 0.04737 |
2 | 17.64177 | 8.77836 | 0.00236 | 0.05682 |
3 | 15.46858 | 8.86537 | 0.00235 | 0.06480 |
4 | 13.99343 | 8.93115 | 0.00234 | 0.07163 |
5 | 12.92932 | 8.98279 | 0.00234 | 0.07752 |
6 | 12.12863 | 9.02441 | 0.00233 | 0.08264 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
53 | 8.32612 | 9.26821 | 0.00233 | 0.12038 |
54 | 8.32504 | 9.26830 | 0.00233 | 0.12040 |
55 | 8.32407 | 9.26837 | 0.00233 | 0.12041 |
56 | 8.32322 | 9.26844 | 0.00233 | 0.12043 |
57 | 8.32246 | 9.26850 | 0.00233 | 0.12044 |
58 | 8.32178 | 9.26855 | 0.00233 | 0.12045 |
59 | 8.32118 | 9.26860 | 0.00233 |
|
60 | 8.32065 | 9.26864 | 0.00233 | 0.12046 |
