Complete Monotonicity of Modified Bessel Functions
نویسندگان
چکیده
منابع مشابه
A monotonicity property of Bessel functions
We extend and unify the proof of a result of L. Lorch (Rend. Sem. Mat. Univ. Politec. Torino 50 (1992), 209–216) by showing that the ratio sgn(ν)Jν+1(|ν|)/Jν(|ν|) increases from −∞ to 1 as ν increases from ν0 (= −0.8375 . . .) to ∞. Here ν0 is the largest zero of Jν(|ν|). One approach is based on an expansion of this ratio involving Rayleigh sums. Another is based on a continued fraction repres...
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In the paper, the authors verify the complete monotonicity of the difference e − ψ′(t) on (0,∞), compute the completely monotonic degree and establish integral representations of the remainder of the Laurent series expansion of e, and derive an inequality which gives a lower bound for the first order modified Bessel function of the first kind. These results show us some new properties and relat...
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Let [Formula: see text] with [Formula: see text] be the modified Bessel functions of the first kind of order v. In this paper, we prove the monotonicity of the function [Formula: see text] on [Formula: see text] for different values of parameter p with [Formula: see text]. As applications, we deduce some new Simpson-Spector-type inequalities for [Formula: see text] and derive a new type of boun...
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A theorem ofLorch, Muldoon and Szeg0 states that the sequence
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Some power series representations of the modified Bessel functions (McDonald functions Kα) are derived using the little known formalism of fractional derivatives. The resulting summation formulae are believed to be new. 1 Fractional derivatives There are several non-trivial examples in mathematics when some quantity, originally defined as integer, can radically extend its original range and ass...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1990
ISSN: 0002-9939
DOI: 10.2307/2048282