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# Computation of Modified Bessel Functions and Their Ratios

D. E. Amos
Mathematics of Computation
Vol. 28, No. 125 (Jan., 1974), pp. 239-251
DOI: 10.2307/2005830
Stable URL: http://www.jstor.org/stable/2005830
Page Count: 13
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## Abstract

An efficient algorithm for calculating ratios $r_\nu(x) = I_{\nu+1}(x)/I_\nu(x), \nu \geqq 0, x \geqq 0$, is presented. This algorithm in conjunction with the recursion relation for $r_\nu(x)$ gives an alternative to other recursive methods for $I_\nu(x)$ when approximations for low-order Bessel functions are available. Sharp bounds on $r_\nu(x)$ and $I_\nu(x)$ are also established in addition to some monotonicity properties of $r_\nu(x)$ and $r_\nu'(x)$.

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