Some numerical methods for approximating modified Bessel functions

Some Inequalities for Modified Bessel Functions

We denote by Iν and Kν the Bessel functions of the first and third kind, respectively. Motivated by the relevance of the function wν t t Iν−1 t /Iν t , t > 0, in many contexts of applied mathematics and, in particular, in some elasticity problems Simpson and Spector 1984 , we establish new inequalities for Iν t /Iν−1 t . The results are based on the recurrence relations for Iν and Iν−1 and the ...

Some 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...

Analysis and Applications of Some Modified Bessel Functions

Some new properties of kernels of modified Kontorovitch–Lebedev integral transforms — modified Bessel functions of the second kind with complex orderK 1 2+iβ (x) are presented. Inequalities giving estimations for these functions with argument x and parameter β are obtained. The polynomial approximations of these functions as a solutions of linear differential equations with polynomial coefficie...

Some Distributions Involving Bessel Functions

On approximating the modified Bessel function of the second kind

In the article, we prove that the double inequalities [Formula: see text] hold for all [Formula: see text] if and only if [Formula: see text] and [Formula: see text] if [Formula: see text], where [Formula: see text] is the modified Bessel function of the second kind. As applications, we provide bounds for [Formula: see text] with [Formula: see text] and present the necessary and sufficient cond...