Redheffer type bounds for Bessel and modified Bessel functions of the first kind
نویسندگان
چکیده
منابع مشابه
Redheffer Type Inequality for Bessel Functions
In this short note, by using mathematical induction and infinite product representations of the functions Jp : R → (−∞, 1] and Ip : R → [1,∞), defined by Jp(x) = 2Γ(p + 1)xJp(x) and Ip(x) = 2Γ(p + 1)xIp(x), an extension of Redheffer’s inequality for the function Jp and a Redheffer-type inequality for the function Ip are established. Here Jp and Ip, denotes the Bessel function and modified Besse...
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For ν an unrestricted real (or complex) number, let Iν be the modified Bessel function of the first kind of order ν, defined by [1, p. 77] Iν(x) = ∑ n≥0 (x/2)2n+ν n!0(ν + n+ 1) , which occurs frequently in problems of electrical engineering, finite elasticity, quantum billiards, wave mechanics, mathematical physics and chemistry, etc. Here x is an arbitrary real (or complex) number, and as usua...
متن کاملFunctional inequalities involving Bessel and modified Bessel functions of the first kind
In this paper, we extend some known elementary trigonometric inequalities, and their hyperbolic analogues to Bessel and modified Bessel functions of the first kind. In order to prove our main results, we present some monotonicity and convexity properties of some functions involving Bessel and modified Bessel functions of the first kind. We also deduce some Turán and Lazarević-type inequalities ...
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Outline Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
متن کاملUniform Bounds for Bessel Functions
For ν > −1/2 and x real we shall establish explicit bounds for the Bessel function Jν(x) which are uniform in x and ν. This work and the recent result of L. J. Landau [7] provide relatively sharp inequalities for all real x.
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ژورنال
عنوان ژورنال: Aequationes mathematicae
سال: 2018
ISSN: 0001-9054,1420-8903
DOI: 10.1007/s00010-018-0545-8