Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications
Let $I_{v}\left( x\right) $ be modified Bessel functions of the first kind. We prove the monotonicity property of the function $x\mapsto I_{u}\left( x\right) I_{v}\left( x\right) /I_{\left( u+v\right) /2}\left( x\right) ^{2}$ on $\left( 0,\infty \right) $. As a direct consequence, it deduces some kn...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/698 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/698 |
| Access Level: | acceso embargado |
| Palabra clave: | Modified Bessel functions of the first kind Monotonicity convexity functional inequality Turán type inequality |
| Sumario: | Let $I_{v}\left( x\right) $ be modified Bessel functions of the first kind. We prove the monotonicity property of the function $x\mapsto I_{u}\left( x\right) I_{v}\left( x\right) /I_{\left( u+v\right) /2}\left( x\right) ^{2}$ on $\left( 0,\infty \right) $. As a direct consequence, it deduces some known results including Tur\'{a}n-type inequalities and log-convexity or log-concavity of $I_{v}$ in $v$, as well as it yields some new and interesting monotonicity and convexity concerning the ratios of modified Bessel functions of the first kind. In addition, a few of sharp bounds involving $I_{v}\left( x\right) $ and their ratios are presented. |
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