Theory and Modern Applications
Table 4 Some numerical results for calculation of \(\varLambda _{1}\) and \(\varLambda _{2}\) with \(q=\frac{1}{3}\) and \(n=1, 2, \ldots , 12\) of Example 2
n | \(\varGamma _{q}(2-\beta )\) | \(\varGamma _{q}(\alpha -\beta )\) | \(\varGamma _{q}(\alpha )\) | \(\varLambda _{1}\) | \(\varLambda _{2}\) |
|---|---|---|---|---|---|
1 | 0.988977 | 1.038462 | 1.105539 | −1.110973 | −0.871523 |
2 | 0.968078 | 1.0125 | 1.074674 | −1.146096 | −0.90379 |
3 | 0.961333 | 1.004132 | 1.064736 | −1.15789 | −0.914692 |
4 | 0.959108 | 1.001374 | 1.061461 | −1.16183 | −0.918342 |
5 | 0.958369 | 1.000457 | 1.060373 | −1.163145 | −0.919561 |
6 | 0.958123 | 1.000152 | 1.060011 | −1.163583 | −0.919967 |
7 | 0.958041 | 1.000051 | 1.059891 | −1.16373 | −0.920103 |
8 | 0.958014 | 1.000017 | 1.05985 | −1.163778 | −0.920148 |
9 | 0.958005 | 1.000006 | 1.059837 | −1.163794 | −0.920163 |
10 | 0.958002 | 1.000002 | 1.059832 | −1.1638 | −0.920168 |
11 | 0.958001 | 1.000001 | 1.059831 | −1.163802 | −0.92017 |
12 | 0.958 | 1 | 1.05983 | −1.163802 | −0.92017 |