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

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.

 Autoría: Ruiz-Antolín D., Segura J.,

 Fuente: Journal of Mathematical Analysis and Applications, Volume 443, Issue 2, 15 November 2016, Pages 1232-1246

 Editorial: Academic Press Inc.

 Fecha de publicación: 15/11/2016

 Nº de páginas: 14

 Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.jmaa.2016.06.011

 ISSN: 0022-247X,1096-0813

 Proyecto español: MTM2012-34787

 Url de la publicación: https://doi.org/10.1016/j.jmaa.2016.06.011