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

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...

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Detalhes bibliográficos
Autores: Ruiz Antolín, Diego|||0000-0001-8011-6529, Segura Sala, José Javier|||0000-0002-0841-5636
Formato: artículo
Fecha de publicación:2016
País:España
Recursos:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/11337
Acesso em linha:http://hdl.handle.net/10902/11337
Access Level:acceso abierto
Palavra-chave:Modified Bessel functions
Bounds
Descrição
Resumo: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.