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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Computation of modified Bessel functions and their ratios

Author: D. E. Amos
Journal: Math. Comp. 28 (1974), 239-251
MSC: Primary 33A40; Secondary 65D20
MathSciNet review: 0333287
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Abstract: An efficient algorithm for calculating ratios ${r_v}(x) = {I_{v + 1}}(x)/{I_v}(x),v \geqq 0,x \geqq 0$, is presented. This algorithm in conjunction with the recursion relation for ${r_v}(x)$ gives an alternative to other recursive methods for ${I_v}(x)$ when approximations for low-order Bessel functions are available. Sharp bounds on ${r_v}(x)$ and ${I_v}(x)$ are also established in addition to some monotonicity properties of ${r_v}(x)$ and $r’_{v}(x)$.

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Keywords: Modified Bessel functions, recursive computation, ratios of Bessel functions, bounds on Bessel functions
Article copyright: © Copyright 1974 American Mathematical Society