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arXiv · 1606.02008

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

D. Ruiz-Antolin·J. Segura
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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 shaper 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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D. Ruiz-Antolin, J. Segura. 2016-06-07. A new type of sharp bounds for ratios of modified Bessel functions. https://arxiv.org/abs/1606.02008

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