A new type of sharp bounds for ratios of modified Bessel functions

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URI: http://hdl.handle.net/10902/11337
ISSN: 0022-247X
ISSN: 1096-0813
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Autoría
Ruiz Antolín, DiegoAutoridad Unican; Segura Sala, José JavierAutoridad Unican
Fecha
2016-11-15
Derechos
© 2016, Elsevier. Licensed under the Creative Commons Reconocimiento-NoComercial-SinObraDerivada
Publicado en
Journal of Mathematical Analysis and Applications, Volume 443, Issue 2, 15 November 2016, Pages 1232-1246
Editorial
Academic Press Inc.
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Palabras clave
Modified Bessel functions
Bounds
Resumen/Abstract
The bounds for the ratios of first and second kind modified Bessel functions of consecutive orders are important quantities appearing in a large number of scientific applications. We obtain new bounds which are accurate in a large region of parameters and which are sharper than previous bounds. The new bounds are obtained by a qualitative analysis of the Riccati equation satisfied by these ratios. A procedure is considered in which the bounds obtained from the analysis of the Riccati equation are used to define a new function satisfying a new Riccati equation which yields sharper bounds. Similar ideas can be applied to other functions.
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© 2016, Elsevier. Licensed under the Creative Commons Reconocimiento-NoComercial-SinObraDerivadaExcepto si se señala otra cosa, la licencia del ítem se describe como © 2016, Elsevier. Licensed under the Creative Commons Reconocimiento-NoComercial-SinObraDerivada