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: |
Bolyai Institute, University of Szeged
Szeged
2019
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| Sorozat: | Acta scientiarum mathematicarum
85 No. 1-2 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-018-263-5 |
| Online Access: | http://acta.bibl.u-szeged.hu/62140 |
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| 024 | 7 | |a 10.14232/actasm-018-263-5 |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Alzer Horst | |
| 245 | 1 | 2 | |a A monotonicity property of the Mittag-Leffler function |h [elektronikus dokumentum] / |c Alzer Horst |
| 260 | |a Bolyai Institute, University of Szeged |b Szeged |c 2019 | ||
| 300 | |a 181-187 | ||
| 490 | 0 | |a Acta scientiarum mathematicarum |v 85 No. 1-2 | |
| 520 | 3 | |a 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. | |
| 650 | 4 | |a Természettudományok | |
| 650 | 4 | |a Matematika | |
| 695 | |a Matematika | ||
| 700 | 0 | 1 | |a Kwong Man Kam |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/62140/1/math_085_numb_001-002_181-187.pdf |z Dokumentum-elérés |