A monotonicity property of the Mittag-Leffler function
Let Fα,β(x) = βEβ(x ) − αEα(x ), where Eα denotes the Mittag– Leffler function. We prove that if α, β ∈ (0, 1], then Fα,β is completely monotonic on (0, ∞) if and only if α ≤ β. This extends a result of T. Simon, who proved in 2015 that Fα,1 is completely monotonic on (0, ∞) if α ∈ (0, 1]. Moreover,...
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2019
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| Sorozat: | Acta scientiarum mathematicarum
85 No. 1-2 |
| Kulcsszavak: | Matematika |
| doi: | 10.14232/actasm-018-263-5 |
| Online Access: | http://acta.bibl.u-szeged.hu/62140 |
| Tartalmi kivonat: | Let Fα,β(x) = βEβ(x ) − αEα(x ), where Eα denotes the Mittag– Leffler function. We prove that if α, β ∈ (0, 1], then Fα,β is completely monotonic on (0, ∞) if and only if α ≤ β. This extends a result of T. Simon, who proved in 2015 that Fα,1 is completely monotonic on (0, ∞) if α ∈ (0, 1]. Moreover, we apply our monotonicity theorem to obtain some functional inequalities involving Fα,β. |
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| Terjedelem/Fizikai jellemzők: | 181-187 |
| ISSN: | 2064-8316 |