An efficient automatic quadrature procedure is developed for numerically computing the integrals 0 , where the function is smooth and nonoscillatory at infinity and is the Bessel functions of order ν =1,0 and 1/4. The procedure involves the use of an automatic integration scheme of modified FFT used for evaluating Fourier integrals and product type integration, and the modified W-transformation...

In the paper, the authors verify the complete monotonicity of the difference e − ψ′(t) on (0,∞), compute the completely monotonic degree and establish integral representations of the remainder of the Laurent series expansion of e, and derive an inequality which gives a lower bound for the first order modified Bessel function of the first kind. These results show us some new properties and relat...

This paper is an attempt is made to obtain Generating functions of modified Bessel Function. We can find number of generating functions for various special function and orthogonal polynomials by the application of group-theoretic method introduced by Louis Weisner.The process may also lead to some new generating functions for corresponding special functions. Bessel Function and orthogonal polyn...

This paper presents the transient solution of a variant working vacation queue with balking. Customers arrive according to a Poisson process and decide to join the queue with probability $b$ or balk with $bar{b} = 1-b$. As soon as the system becomes empty, the server takes working vacation. The service times during regular busy period and working vacation period, and vacation times are assumed ...

This paper studies axially symmetric vibrations of a liquid-filled poroelastic thin cylinder saturated with two immiscible liquids of infinite extent that is surrounded by an inviscid elastic liquid. By considering the stress free boundaries, the frequency equation is obtained. Particular case, namely, liquid-filled poroelastic cylinder saturated with single liquid is discussed.  When the waven...

We give a shorter proof of Kanter's (1976) sharp Bessel function bound for concentrations of sums of independent symmetric random vectors. We provide sharp upper bounds for the sum of modified Bessel functions I 0 (x) + I 1 (x), which might be of independent interest. Corollaries improve concentration or smoothness bounds for sums of independent random variables due toČekanavičius

This paper is part of the collection initiated in [12], aiming to evaluate the entries in [8] and to provide some context. This table contains a large variety of entries involving the Bessel functions. The goal of the current work is to evaluate some entries in [8] where the integrand is an elementary function and the result involves the so-called modified Bessel function of the second kind, de...

The transformation from a time-dependent random walk to quantum mechanics converts a modi­ fied Bessel function into an ordinary one together with a phase factor e,ir/2 for each time the electron flips both direction and handedness. Causality requires the argument to be greater than the order of the Bessel function. Assuming equal probabilities for jumps ± 1 , the normalized modified Bessel fun...

Let Iν and Kν denote the modified Bessel functions of the first and second kinds of order ν. In this note we prove that the monotonicity of u → Iν(u)Kν(u) on (0,∞) for all ν ≥ −1/2 is an almost immediate consequence of the corresponding Turán type inequalities for the modified Bessel functions of the first and second kinds of order ν. Moreover, we show that the function u → Iν(u)Kν(u) is strict...