Computation of modified Bessel functions and their 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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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: 1974
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1974-0333287-7