A new three-dimensional integral containing f(x,y,z)Iv(x?) is derived where Iv(x?) the Modified Bessel Function of first kind and taken over infinite cubic space 0<x<?,0<y<?,0<z<?. The not easily evaluated for complex ranges parameters. representation in terms Hurwitz–Lerch zeta function, polylogarithm function Riemann functions are evaluated. This yields triple representation...

In this paper, we show that the matrix elements of some Lorentz group representation operators and bases transform acting in space may be expressed terms modified Bessel–Clifford functions their multi-index analogs introduced by authors via Delerue hyper Bessel functions.

By using the three-term recurrence equation satisfied by a family of orthogonal polynomials, the Christoffel-Darboux-type bilinear generating function and their asymptotic expressions, we obtain quadrature formulas for integral transforms generated by the classical orthogonal polynomials. These integral transforms, related to the so-called Poisson integrals, correspond to a modified Fourier Tra...

We find low order approximations to the spherical nonreflecting boundary kernel for the wave equation in three dimensions. First we express the Laplace transform of the kernel as a rational function by solving for the zeros of a modified Bessel function. Then we formulate a linear time-invariant dynamical system whose transfer function is this rational function. Finally we use the Balanced Trun...

Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases, we show that we obtain the best possible constant or that our bounds are tight in certain limits. We apply these inequalities to obtain uniform bounds for several expressions involving integrals of modified Bessel functions. Such expressions occur in Stein’...

in this paper, we establish some new results in ultra bessel sequences and ultra bessel sequences of subspaces. also, we investigate ultra bessel sequences in direct sums of hilbert spaces.specially, we show that {( fi, gi)}∞ i=1 is a an ultra bessel sequencefor hilbert space h ⊕ k if and only if { fi}∞ i=1 and {gi}∞ i=1 are ultrabessel sequences for hilbert spaces h and k, respectively.

This paper proposes new bounds for Marcum Q-function, which prove extremely tight and outperform all the bounds previously proposed in the literature. What is more, the proposed bounds are good and stable both for large values and small values of the parameters of the Marcum Q-function, where the previously introduced bounds are bad and even useless under some conditions. The new bounds are der...

On two pages in his lost notebook, Ramanujan recorded several theorems involving the modified Bessel function Kν(z). These include Koshliakov’s formula and Guinand’s formula, both connected with the functional equation of nonanalytic Eisenstein series, and both discovered by these authors several years after Ramanujan’s death. Other formulas, including one by K. Soni and two particularly elegan...

The joint probability density function of a random vector (Y1, Y2) following Kibble’s bivariate gamma distribution (BGD) with parameters α, μ1, μ2 and ρ, is given by fY1,Y2(y1, y2) = (μ1μ2) α (1− ρ)Γ(α) ( y1y2 ρμ1μ2 )α−1 2 exp ( − μ1y1 + μ2y2 1− ρ ) Iα−1 ( 2 √ ρμ1μ2y1y2 1− ρ ) , for y1 > 0, y2 > 0, where Γ(α) is the gamma function defined as Γ(α) = ∫∞ 0 t α−1e−tdt, and Iα(·) is the modified Bes...