Powers of modified Bessel functions of the first kind
نویسندگان
چکیده
منابع مشابه
Powers of modified Bessel functions of the first kind
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 ...
متن کاملMonotonicity of the ratio of modified Bessel functions of the first kind with applications
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 کاملBessel Functions of the First and Second Kind
Outline Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
متن کاملCalculation of the Modified Bessel Functions of the Second Kind with Complex Argument
In physical problems often the modified Bessel functions Kniz) with complex argument z occur, or the Hankel functions of the first kind Hn\z) which are related to Kniz) hyKniz) = iir/2)in+1Hna\iz), with i = (-l)m. Computationally rapid and fairly exact procedures are available for the evaluation of these functions for real or imaginary argument either by recurrence, [1], [2], or by polynomial a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2010
ISSN: 0893-9659
DOI: 10.1016/j.aml.2010.02.015