Theory and Modern Applications
Table 5 Some numerical results for calculation of \(\varLambda _{1}\) and \(\varLambda _{2}\) with \(q=\frac{1}{2}\) and \(n=1, 2, \ldots , 19\) of Example 2
n | \(\varGamma _{q}(2-\beta )\) | \(\varGamma _{q}(\alpha -\beta )\) | \(\varGamma _{q}(\alpha )\) | \(\varLambda _{1}\) | \(\varLambda _{2}\) |
|---|---|---|---|---|---|
1 | 1.05421 | 1.142857 | 1.261962 | −0.97516 | −0.76776 |
2 | 0.996499 | 1.066667 | 1.165469 | −1.062079 | −0.845235 |
3 | 0.970276 | 1.032258 | 1.122114 | −1.106468 | −0.885437 |
4 | 0.957751 | 1.015873 | 1.101521 | −1.128899 | −0.905919 |
5 | 0.951628 | 1.007874 | 1.09148 | −1.140174 | −0.916256 |
6 | 0.9486 | 1.003922 | 1.086522 | −1.145827 | −0.921449 |
7 | 0.947094 | 1.001957 | 1.084058 | −1.148657 | −0.924052 |
8 | 0.946343 | 1.000978 | 1.08283 | −1.150073 | −0.925354 |
9 | 0.945968 | 1.000489 | 1.082217 | −1.150782 | −0.926006 |
10 | 0.945781 | 1.000244 | 1.081911 | −1.151136 | −0.926332 |
11 | 0.945687 | 1.000122 | 1.081758 | −1.151313 | −0.926495 |
12 | 0.945641 | 1.000061 | 1.081681 | −1.151401 | −0.926577 |
13 | 0.945617 | 1.000031 | 1.081643 | −1.151446 | −0.926618 |
14 | 0.945606 | 1.000015 | 1.081624 | −1.151468 | −0.926638 |
15 | 0.9456 | 1.000008 | 1.081614 | −1.151479 | −0.926648 |
16 | 0.945597 | 1.000004 | 1.081609 | −1.151485 | −0.926653 |
17 | 0.945595 | 1.000002 | 1.081607 | −1.151487 | −0.926656 |
18 | 0.945595 | 1.000001 | 1.081606 | −1.151489 | −0.926657 |
19 | 0.945594 | 1.000000 | 1.081605 | −1.151489 | −0.926658 |