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On the Computation of Modified Bessel Function Ratios

Walter Gautschi and Josef Slavik
Mathematics of Computation
Vol. 32, No. 143 (Jul., 1978), pp. 865-875
DOI: 10.2307/2006491
Stable URL: http://www.jstor.org/stable/2006491
Page Count: 11
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Abstract

A detailed comparison is made between a continued fraction of Gauss, and one of Perron, for the evaluation of ratios of modified Bessel functions $I_\nu(x)/I_{\nu-1}(x), x > 0, \nu > 0$. It will be shown that Perron's continued fraction has remarkable advantages over Gauss' continued fraction, particularly when $x \gg \nu$.

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