In a previous study, we discussed the expansion of two-parameter functions in a double series of Chebyshev polynomials, and, in particular, we presented coefficients for the evaluation of the modified Bessel function (2z I iifne'K,(z) to 20 decimals for all z ^ 5 and all v, 0 g v g 1. In the present study, we give similar coefficients for the evaluation of ge~'z-»l,(z) to at least 20 decimals w...

Calcium [Ca] dynamics is studied as a potential form of neuron excitability that can control many irregular processes like metabolism, secretion etc. Ca ion enters presynaptic terminal and increases the synaptic strength and thus triggers the neurotransmitter release. The modeling and analysis of calcium dynamics in neuron cell becomes necessary for deeper understanding of the processes involve...

In this note our aim is to point out that certain inequalities for modified Bessel functions of the first and second kind, deduced recently by Laforgia and Natalini, are in fact equivalent to the corresponding Turán type inequalities for these functions. Moreover, we present some new Turán type inequalities for the aforementioned functions and we show that their product is decreasing as a funct...

The aim of this paper is to study the mixture of the Riesz distribution on symmetric matrices with respect to the multivariate Poisson distribution. We show, in particular, that this distribution is related to the modified Bessel function of the first kind. We also study the generated natural exponential family. We determine the domain of the means and the variance function of this family.

The aim of this paper is to study the mixture of the Riesz distribution on symmetric matrices with respect to the multivariate Poisson distribution. We show, in particular, that this distribution is related to the modified Bessel function of the first kind. We also study the generated natural exponential family. We determine the domain of the means and the variance function of this family.

In this short note, by using mathematical induction and infinite product representations of the functions Jp : R → (−∞, 1] and Ip : R → [1,∞), defined by Jp(x) = 2Γ(p + 1)xJp(x) and Ip(x) = 2Γ(p + 1)xIp(x), an extension of Redheffer’s inequality for the function Jp and a Redheffer-type inequality for the function Ip are established. Here Jp and Ip, denotes the Bessel function and modified Besse...

We give a number field analogue of result Ramanujan, Hardy and Littlewood, thereby obtaining modular relation involving the non-trivial zeros Dedekind zeta function. also provide Riesz-type criterion for Generalized Riemann Hypothesis ζK(s). New elegant transformations are obtained when K is quadratic extension, one which involves modified Bessel function second kind.

Abstract Discrete analogues of the index transforms, involving Bessel and modified functions, are introduced investigated. The corresponding inversion theorems for suitable classes functions sequences established.

The scintillation index is formulated for modified Bessel-Gaussian beams propagating in weakly turbulent media. Numerical calculations applied directly to the derived triple integral show that, for off-axis positions, the modified Bessel-Gaussian beams of higher than zero order scintillate less than Gaussian beams at large input beam sizes and low beam orders with the increasing width parameter...