Table 1 Some numerical results for \(\varSigma _{1}\), \(\varSigma _{2}\), and \(\varSigma _{3}\) in Example 1 for \(q=\frac{1}{10}, \frac{1}{2}, \frac{6}{7}\)
n | \(q =\frac{1}{10}\) | \(q =\frac{1}{2}\) | \(q =\frac{6}{7}\) | ||||||
|---|---|---|---|---|---|---|---|---|---|
\(\varSigma _{1}\) | \(\varSigma _{2}\) | \(\varSigma _{3}\) | \(\varSigma _{1}\) | \(\varSigma _{2}\) | \(\varSigma _{3}\) | \(\varSigma _{1}\) | \(\varSigma _{2}\) | \(\varSigma _{3}\) | |
1 | −0.3442 | −0.3434 | −0.3409 | −0.3142 | −0.2946 | −0.2815 | −0.1587 | −0.0793 | −0.0596 |
2 | −0.3446 | −0.3439 | −0.3414 | −0.3381 | −0.326 | −0.3147 | −0.1837 | −0.1125 | −0.09 |
3 | −0.3446 | −0.344 | −0.3414 | −0.3501 | −0.342 | −0.3317 | −0.2076 | −0.1435 | −0.1197 |
4 | −0.3446 | −0.344 | −0.3414 | −0.3562 | −0.35 | −0.3403 | −0.2292 | −0.1716 | −0.1476 |
5 | −0.3446 | −0.344 | −0.3414 | −0.3592 | −0.3541 | −0.3446 | −0.2484 | −0.1968 | −0.1731 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
10 | −0.3446 | −0.344 | −0.3414 | −0.3622 | −0.358 | −0.3488 | −0.3128 | −0.2832 | −0.2634 |
11 | −0.3446 | −0.344 | −0.3414 | −0.3622 | −0.3581 | −0.3489 | −0.3209 | −0.2943 | −0.2752 |
12 | −0.3446 | −0.344 | −0.3414 | −0.3622 | −0.3581 | −0.3489 | −0.3279 | −0.3039 | −0.2855 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
56 | −0.3446 | −0.344 | −0.3414 | −0.3622 | −0.3581 | −0.3489 | −0.3706 | −0.3626 | −0.3487 |
57 | −0.3446 | −0.344 | −0.3414 | −0.3622 | −0.3581 | −0.3489 | −0.3706 | −0.3627 | −0.3488 |
58 | −0.3446 | −0.344 | −0.3414 | −0.3622 | −0.3581 | −0.3489 | −0.3706 | −0.3627 | −0.3488 |
59 | −0.3446 | −0.344 | −0.3414 | −0.3622 | −0.3581 | −0.3489 | −0.3707 | −0.3627 | −0.3488 |
60 | −0.3446 | −0.344 | −0.3414 | −0.3622 | −0.3581 | −0.3489 | −0.3707 | −0.3627 | −0.3488 |