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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A theorem ofLorch, Muldoon and Szeg0 states that the sequence
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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...
متن کاملSome Integrals Involving Bessel Functions Some Integrals Involving Bessel Functions
A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized hypergeometric function with subsequent reduction to special cases. Connection is made with Weber's second exponential integral and Laplace transforms of pr...
متن کاملUnivalence of Bessel Functions
In particular we shall first determine a radius of univalence for the normalized Bessel functions [7>(z)]1/" for values of v belonging to the region G defined by the inequalities 6{\v} >0, | arg »»| <7r/4. Then we shall determine the radius of univalence of the functions z1_"7,.(z) for values of v belonging to a subset of the closure of G. When v is real and positive we shall determine the exac...
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ژورنال
عنوان ژورنال: SIAM Review
سال: 1987
ISSN: 0036-1445,1095-7200
DOI: 10.1137/1029078