It should be remarked that asymptotic estimates of the behavior of the sine and of other integral transforms of regularly varying functions [6] in terms of the function f (1/x) had been obtained before [7–9], both as x → 0 and as x →∞. However, (1.1) is a global estimate that not only considers the endpoint behavior but also holds for all x > 0. Our aim in this article is to generalize (1.1) in...

Generalization of the integral representation gamma function has been obtained, which shows that Hankel contour assumes rotation in complex plane. The range admissible values for angle is set. Using this representation, generalization Mittag-Leffler obtained expresses value terms integral.

Many standard conversion matrices between coefficients in classical orthogonal polynomial expansions can be decomposed using diagonally-scaled Hadamard products involving Toeplitz and Hankel matrices. This allows us to derive O(N(logN)) algorithms, based on the fast Fourier transform, for converting coefficients of a degree N polynomial in one polynomial basis to coefficients in another. Numeri...

The significance of the similarity theorem for the fractional Fourier transform is discussed, and the properties of self-similar functions considered. The concept of the fractional Hankel transform is developed for use in the analysis of diffraction and imaging in symmetrical optical systems. The particular case of Fresnel diffraction from a circular aperture is discussed and the effects of the...

Asymptotic behavior of the integral '((w) = r e-"%(wx)f(x2)xdx is investigated, where J0(x) is the Bessel function of the first kind and w is a large positive parameter. It is shown that IAw) decays exponentially like e~y"' , y > 0, when/(z) is an entire function subject to a suitable growth condition. A complete asymptotic expansion is obtained when /( z ) is a meromorphic function satisfying ...

In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

The elasticity mixed boundary values problems dealing with half-space contact are generally well resolved. A large number of these solutions are obtained by using the integral transformation method and methods based the integral equations. However, the problems of finite layer thicknesses are less investigated, despite their practical interests. This study resolves a quasi-stationary problem of...

For random selfadjoint (real symmetric, complex Hermitian, or quaternion self-dual) Toeplitz matrices and real symmetric Hankel matrices, the existence of universal limit distributions for eigenvalues and products of several independent matrices is proved. The joint moments are the integral sums related to certain pair partitions. Our method can apply to random Hankel and Toeplitz band matrices...

with u0 = 0, where the dot indicates differentiation with respect to t. In this note, we shall show how solutions to this equation can be formulated in the context of exponential Riordan arrays. The Riordan arrays we shall consider may be considered as parameterised (or “time”-dependent) Riordan arrays. We have already considered parameterized Riordan arrays [1], exploring the links between the...

In this note we announce an extension of these theorems to the setting of Stiefel manifolds and matrix space. Our work makes it possible to construct holomorphic discrete series representations for the real symplectic group by decomposing a tensor product of certain projective representations introduced earlier by Shale and Weil. (See Weil [11] and also Shalika [10].) Proofs of the results anno...