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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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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1974-0333287-7
Keywords: Modified Bessel functions, recursive computation, ratios of Bessel functions, bounds on Bessel functions
Article copyright: © Copyright 1974 American Mathematical Society