Theory and Modern Applications
n | \(\mathcal{I}_{q}^{\alpha }[m_{1}] (t)\) | \(\mathcal{I}_{q}^{\alpha +1} [m_{1}] (1)\) | \(\mathcal{I}_{q}^{\alpha -1} [m_{1}] (s)\) | ||||
---|---|---|---|---|---|---|---|
t = 0 | t = 1 | sup | s = 1 | s = a | s = b | ||
\(q = \frac{1}{8}\) | |||||||
1 | 0 | 0.0516 | 0.0516 | 0.0454 | 0.0556 | 0.0404 | 0.0561 |
2 | 0 | 0.0527 | 0.0527 | 0.0465 | 0.0564 | 0.0408 | 0.0569 |
3 | 0 | 0.0529 | 0.0529 | 0.0466 | 0.0565 | 0.0409 | 0.0570 |
4 | 0 | 0.0529 | 0.0529 | 0.0466 | 0.0566 | 0.0409 | 0.057 |
\(q = \frac{1}{2}\) | |||||||
1 | 0 | 0.0347 | 0.0347 | 0.0196 | 0.0515 | 0.0362 | 0.0514 |
2 | 0 | 0.0446 | 0.0446 | 0.0265 | 0.0586 | 0.0399 | 0.0576 |
3 | 0 | 0.0499 | 0.0499 | 0.0305 | 0.062 | 0.0416 | 0.0605 |
4 | 0 | 0.0526 | 0.0526 | 0.0325 | 0.0636 | 0.0424 | 0.062 |
5 | 0 | 0.0539 | 0.0539 | 0.0336 | 0.0644 | 0.0428 | 0.0627 |
6 | 0 | 0.0546 | 0.0546 | 0.0341 | 0.0649 | 0.043 | 0.063 |
7 | 0 | 0.055 | 0.055 | 0.0344 | 0.0651 | 0.0431 | 0.0632 |
8 | 0 | 0.0552 | 0.0552 | 0.0345 | 0.0652 | 0.0432 | 0.0633 |
9 | 0 | 0.0552 | 0.0552 | 0.0346 | 0.0652 | 0.0432 | 0.0633 |
\(q = \frac{6}{7}\) | |||||||
1 | 0 | 0.0067 | 0.0067 | 0.0013 | 0.0293 | 0.0216 | 0.0298 |
2 | 0 | 0.011 | 0.011 | 0.0025 | 0.0363 | 0.0261 | 0.0366 |
3 | 0 | 0.0154 | 0.0154 | 0.004 | 0.0418 | 0.0294 | 0.0418 |
â‹® | â‹® | â‹® | â‹® | â‹® | â‹® | â‹® | â‹® |
37 | 0 | 0.0551 | 0.0551 | 0.0257 | 0.0705 | 0.0446 | 0.0673 |
38 | 0 | 0.0551 | 0.0551 | 0.0257 | 0.0705 | 0.0447 | 0.0673 |
39 | 0 | 0.0552 | 0.0552 | 0.0257 | 0.0705 | 0.0447 | 0.0673 |
40 | 0 | 0.0552 | 0.0552 | 0.0257 | 0.0705 | 0.0447 | 0.0674 |
41 | 0 | 0.0552 | 0.0552 | 0.0258 | 0.0705 | 0.0447 | 0.0674 |
42 | 0 | 0.0552 | 0.0552 | 0.0258 | 0.0705 | 0.0447 | 0.0674 |
43 | 0 | 0.0553 | 0.0553 | 0.0258 | 0.0706 | 0.0447 | 0.0674 |