Table 2 Comparison of the order of convexity given by Theorems 2, 4 and 6
From: Generalized Lommel–Wright function and its geometric properties
\(\kappa _{1}\) | \(\kappa _{2}\) | \(\kappa _{3}\) | m | \(\widehat{\alpha}_{\max}\) Theorem 2 | \(\widehat{\delta}_{\max}\) Theorem 4 | \(\widehat{\zeta}_{\max}\) Theorem 6 with minγ |
|---|---|---|---|---|---|---|
3 | 2 | 1 | 3 | 0.98930995964631139740 | 0.99476439790575916230 | 0.99607281772648946631 |
7 | 3 | 1 | 4 | 0.99990949804677554452 | 0.99995560882496559684 | 0.99996670645961244179 |
4 | 3 | 2 | 3 | 0.99954682324769373114 | 0.99977772838408535230 | 0.99983329678044753707 |
9 | 6 | 3 | 2 | 0.99999167188683056198 | 0.999995915015992712389 | 0.99999969362732106008 |
5 | 5 | 3 | 4 | 0.99999816657157930414 | 0.99999910069273638516 | 0.9999993255195994225 |
12 | 10 | 5 | 3 | 0.99999999980842471269 | 0.99999999990603118715 | 0.99999999995364882391 |
14 | 13 | 8 | 5 | 0.99999999999999999434 | 0.99999999999999999722 | 0.99999999999999999792 |