"Normal" Distribution Functions on Spheres and the Modified Bessel Functions
نویسندگان
چکیده
منابع مشابه
On a Product of Modified Bessel Functions
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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In this note our aim is to point out that certain inequalities for modified Bessel functions of the first and second kind, deduced recently by Laforgia and Natalini, are in fact equivalent to the corresponding Turán type inequalities for these functions. Moreover, we present some new Turán type inequalities for the aforementioned functions and we show that their product is decreasing as a funct...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1974
ISSN: 0091-1798
DOI: 10.1214/aop/1176996606