Table 4 Some numerical results of \(M(\alpha , b)\) in equation (26) in Example 1 for \(q=\frac{1}{7}, \frac{1}{2}, \frac{8}{9}\)
n | \(q =\frac{1}{7}\) | \(q =\frac{1}{2}\) | \(q =\frac{8}{9}\) | ||||||
|---|---|---|---|---|---|---|---|---|---|
\(A_{1}(\alpha , b) \) | \(A_{2}(\alpha , b)\) | M(α,b) | \(A_{1}(\alpha , b) \) | \(A_{2}(\alpha , b)\) | M(α,b) | \(A_{1}(\alpha , b) \) | \(A_{2}(\alpha , b)\) | M(α,b) | |
1 | 4.8544 | 3.7471 | 4.8544 | 2.4645 | 2.8302 | 2.8302 | 0.1472 | 0.5474 | 0.5474 |
2 | 4.8685 | 3.7575 | 4.8685 | 2.7543 | 3.0915 | 3.0915 | 0.2357 | 0.7566 | 0.7566 |
3 | 4.8705 | 3.759 | 4.8705 | 2.9055 | 3.2248 | 3.2248 | 0.3356 | 0.9602 | 0.9602 |
4 | 4.8708 | 3.7592 | 4.8708 | 2.9826 | 3.292 | 3.292 | 0.4424 | 1.1541 | 1.1541 |
5 | 4.8709 | 3.7592 | 4.8709 | 3.0216 | 3.3258 | 3.3258 | 0.5522 | 1.336 | 1.336 |
â‹® | â‹® | â‹® | â‹® | â‹® | â‹® | â‹® | â‹® | â‹® | â‹® |
15 | 4.8709 | 3.7592 | 4.8709 | 3.0608 | 3.3596 | 3.3596 | 1.4427 | 2.4896 | 2.4896 |
16 | 4.8709 | 3.7592 | 4.8709 | 3.0608 | 3.3597 | 3.3597 | 1.5002 | 2.5526 | 2.5526 |
â‹® | â‹® | â‹® | â‹® | â‹® | â‹® | â‹® | â‹® | â‹® | â‹® |
80 | 4.8709 | 3.7592 | 4.8709 | 3.0608 | 3.3597 | 3.3597 | 2.0086 | 3.0741 | 3.0741 |
91 | 4.8709 | 3.7592 | 4.8709 | 3.0608 | 3.3597 | 3.3597 | 2.0088 | 3.0743 | 3.0743 |
92 | 4.8709 | 3.7592 | 4.8709 | 3.0608 | 3.3597 | 3.3597 | 2.0088 | 3.0744 | 3.0744 |
93 | 4.8709 | 3.7592 | 4.8709 | 3.0608 | 3.3597 | 3.3597 | 2.0089 | 3.0744 | 3.0744 |
94 | 4.8709 | 3.7592 | 4.8709 | 3.0608 | 3.3597 | 3.3597 | 2.0089 | 3.0744 | 3.0744 |