  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.
