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

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• 作者：Diego Ruiz-Antolí ; n ^{diego.ruizantolin@unican.es" class="auth_mail" title="E-mail the corresponding author} ; Javier Segura ; ^{javier.segura@unican.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Modified Bessel functions ; Bounds
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 November 2016
• 年：2016
• 卷：443
• 期：2
• 页码：1232-1246
• 全文大小：377 K

文摘

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.