By considering a particular probabilistic scenario associated with coincidences, we are led to a family of functions akin to the modified Bessel function of the first kind. These are in turn solutions to a certain family of linear differential equations possessing structural similarities to the modified Bessel differential equation. The Stirling number triangle of the second kind arises quite n...

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...

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 ...

In this article, we studied the necessary conditions for univalence of integral operators that involve two functions: generalized Bessel function and a from well-known class normalized analytic functions in open unit disk. The main tools our discussions were Kudriasov univalency functions, as well functional inequalities functions. We included Bessel, modified spherical special cases. Furthermo...

The distribution of the difference between two independent Poisson random variables involves the modified Bessel function of the first kind. Using properties of this function, maximum likelihood estimates of the parameters of the Poisson difference were derived. Asymptotic distribution property of the maximum likelihood estimates is discussed. Maximum likelihood estimates were compared with the...

This paper introduces a new method for the development of closed-form spatial Green’s functions for electrostatic problems involving layered dielectrics. The new method utilizes a finite-difference approximation of the spectral domain form of the Green’s function to overcome the tedious numerical integration of the Fourier–Bessel inverse transform that is required to generate the Green’s functi...

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...

The z-zeros of the modified Bessel function of the third kind Kν(z), also known as modified Hankel function or Macdonald function, are considered for arbitrary complex values of the order ν. Approximate expressions for the zeros, applicable in the cases of very small or very large |ν|, are given. The behaviour of the zeros for varying |ν| or arg ν, obtained numerically, is illustrated by means ...