This paper deals with the helical flow of a Newtonian fluid in an infinite circular cylinder, due to both longitudinal and rotational shear stress. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms and satisfy all imposed initial and boundary conditions. For large times, these solutions reduce to the well-known steady-state sol...

The Euler transformation is a linear sequence transformation to accelerate the convergence of an alternating series. The sequence of weights of the transformation is extended to a continuous weight function which can accelerate Fourier type integrals including Hankel transforms with a slowly convergent integrand. We show that the continuous weight function can also be used to compute the Fourie...

This study considers a class of double finite Hankel transforms that describes the transmission of a vortex optical signal through a two-lens system with limited aperture radii in the object and spectral flats. The eigenfunctions of the given transform are calculated for different orders of vortex m. The functions obtained are an orthonormal system of functions, which can help expand an unspeci...

Using the theory of exponential Riordan arrays and orthogonal polynomials, we demonstrate that the Eulerian polynomials and the shifted Eulerian polynomials are moment sequences for a simple family of orthogonal polynomials. The coefficient arrays of these families of orthogonal polynomials are shown to be exponential Riordan arrays. Using the theory of orthogonal polynomials we are then able t...

A solution of the axisymmetric Boussinesq-type problem is derived for transient thermal stresses in a half-space under heating by using the Laplace and Hankel transforms. An analytical method is developed to predict the temperature field that satisfies the prescribed mechanical conditions. Several simple shapes of punches of arbitrary profile are considered and an expression for the total load ...

Recently Pogány and Süli [Proc. Amer. Math. Soc. 137(7) (2009), 2363–2368] derived a closed-form integral expression for Neumann series of Bessel functions of the first kind Jν . In this paper our aim is to establish analogous integral representations for the Neumann-type series of modified Bessel functions of the first kind Iν and for Bessel functions of the second kind Yν , Kν , and to give l...