[PDF] Top 20 Some Inequalities for Modified Bessel Functions

... t1 − ν ν − 1/2 < 0 which is satisfied for all t > 1/2 − ν/1 − ν when ν > 1. We report here some numerical experiments, computed by using mathematica. Example 3.2. In the first case we assume ν 8. In ... See full document

... special functions are amenable to this analysis, and we give several examples of application: modified Bessel functions, parabolic cylinder functions, Legendre functions of ... See full document

... Yang, Zh-H., Zheng, Sh-Zh.: Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications.. Thiruvenkatachar, V.R., Nanjundiah, T.S.: Inequalities c[r] ... See full document

... the Bessel and modified Bessel differential equations, ...are some extensions of the above mentioned functions in the ...the Bessel and related functions in the recent ... See full document

... Omega functions with equal interval lengths form a set of measure zero within the set of all piece-wise constant Omega functions and, moreover, within all Omega functions admitted by the second ... See full document

... In 2007, Neumann conjectured [4] that the modified Bessel function of the first kind is log-concave on (0, ∞). To the best of our knowledge, it seems to remain an open question [13]. In our investigation, the ... See full document

... As an application of inequality (.), an open problem was proposed, answered and im- proved by Sándor and Bencze in []. Recently, inequality (.) and its related inequalities in [] were extended to ... See full document

... Its general solution is a linear combination of the modified Bessel functions of the first and second kinds... evaluate the propagator at the origin.[r] ... See full document

... the Bessel function and other special functions are of continued interest to the wider scientific ...The Bessel function and its variations have gone through several generalizations, see, for example, ... See full document

... Two-sided inequalities for the theory of special functions ap- pear in the literature of many ...two-sided inequalities are motivated by different problems in mathematics, sciences and engineering ... See full document

... √−1 Bessel function of order n modified Bessel functions half chord length average chord length half chord length at various positions along the span half chord length at wing base numbe[r] ... See full document

... Our final result is based on the Chebyshev integral inequality [26, p. 40], which states the following: suppose f and g are two integrable functions and monotonic in the same sense (either both decreasing or both ... See full document

... We observe that, when σ > 0, the functions f and g defined in the proof of Theorem 3.4 are monotone in the opposite sense. We cannot therefore use Čebyšev inequality to find a lower bound for this case. However, ... See full document

... k-Bessel functions and represents it as Wright func- ...k- Bessel functions, and the ratio of the k-Bessel and the k-Bessel ...hypergeometric functions are ... See full document

... Remark 2.1. The inequality (2.3) is obviously not as good as the first part of (1.12). However it is the natural alternative of Jensen’s inequality for trace and provides simple and nice examples for various convex ... See full document

... Proof Let  < A ≤ B. Fix ε > . We put C = B – A + ε. Let θ > . It follows from lim t→∞ f (t) =  that there exists M >  such that f (t) ≤ θ for all t ≥ M. We may assume that the spectrum of the strictly ... See full document

... Proof. The inequalities P > √ LA and L > √ GP are proved in 10. We will see, that further refinements of these inequalities are true. Now, the second inequality of 3.1 follows by the first inequality ... See full document

... Some sharp Bessel type inequalities for non-orthonormal families of vectors in inner product spaces are given.. Applications for complex numbers are also provided1[r] ... See full document

... preinvex functions on the invex sets in a normed space can be characterized by a class of variational inequalities, which is known as the variational-like ...variational-like inequalities and related ... See full document

... In this paper, we present some sharp inequalities for the ratio of gamma functions. The main tool is the multiple-correction method formulated in (Cao et al. in J. Number Theory 149:327-350, 2015; ... See full document