In this work, we extend the analytic treatment of Bessel functions of large order and/or argument. We examine uniform asymptotic Bessel function expansions and show their accuracy and range of validity. Such situations arise in a variety of applications, in particular the Fourier transform of the gravitational wave signal from a pulsar. The uniform expansion we consider here is found to be vali...

Change in impedance of an encircling coil is obtained in the present paper for the case where the electric conductivity and magnetic permeability of a metal cylindrical tube depend on the radial coordinate. The system of equations for the vector potential is solved by means of the Fourier cosine transform. The solution is expressed in terms of improper integral containing modified Bessel functi...

The problem of scattering of linear internal waves from small compact sea bottom inhomogeneities is considered from the point of view of mode-to-mode scattering. A simple formula for modal conversion coefficients Cnm , quantifying the amount of energy that is scattered into the n-th mode from the incident field m-th mode, is derived. In this formula the representation of inhomogeneities by thei...

The purpose of this paper is to derive closed-form expressions for the error rate performance of coherent H-ary Quadrature Amplitude Modulated (QAM> systems in the presence of an additive combination of Gaussian and highly impulsive noise, using the powerful Fourier-Bessel series expansion method. The emplo:'ed model of the impulsive noise, which closely models atmospheric and/or man-made noise...

In present paper, an initial-boundary value problem is formulated in a rectangle for higher even order partial differential equation with the Bessel operator. Applying method of separation variables to considered spectral obtained ordinary order. The self-adjointness last proved, which implies existence system its eigenfunctions, as well orthonormality and completeness this system. uniform conv...

The helical assembly is a fundamental organization principle of biomacromolecules. To determine the structures of helical filaments or tubes has been helped by the fact that many different views of the helical unit are present to reconstruct a three-dimensional image from a single helix. In this review, I present the current state of helical image reconstruction from electron cryo-micrographs b...

The method of partial Fourier transform is used to find explicit formulas for two remarkable fundamental solutions for a generalized Tricomi operator. These fundamental solutions reflect clearly the mixed type of the Tricomi operator. In proving these results, we establish explicit formulas for Fourier transforms of some functions involving Bessel functions.

In this work, we are interested by the q-Bessel Fourier transform with a new approach. Many important results of this q-integral transform are proved with a new constructive demonstrations and we establish in particular the associated q-Fourier-Neumen expansion which involves the q-little Jacobi polynomials.