On the Computation of Modified Bessel Function Ratios
نویسندگان
چکیده
منابع مشابه
Computation of Modified Bessel Functions and Their Ratios
An efficient algorithm for calculating ratios rv(x) = I,+,(x)/IAx), v â 0, x ä 0, is presented. This algorithm in conjunction with the recursion relation for rAx) gives an alternative to other recursive methods for I Ax) when approximations for low-order Bessel functions are available. Sharp bounds on r,(x) and IAx) are also established in addition to some monotonicity properties of ry(x) and r...
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15 صفحه اولOn approximating the modified Bessel function of the second kind
In the article, we prove that the double inequalities [Formula: see text] hold for all [Formula: see text] if and only if [Formula: see text] and [Formula: see text] if [Formula: see text], where [Formula: see text] is the modified Bessel function of the second kind. As applications, we provide bounds for [Formula: see text] with [Formula: see text] and present the necessary and sufficient cond...
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Let Iν and Kν denote the modified Bessel functions of the first and second kinds of order ν. In this note we prove that the monotonicity of u → Iν(u)Kν(u) on (0,∞) for all ν ≥ −1/2 is an almost immediate consequence of the corresponding Turán type inequalities for the modified Bessel functions of the first and second kinds of order ν. Moreover, we show that the function u → Iν(u)Kν(u) is strict...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1978
ISSN: 0025-5718
DOI: 10.2307/2006491